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Physics

A straight horizontal conducting rod of length $0.45 \mathrm{~m}$ and mass $60 \mathrm{~g}$ is suspended by two vertical wires at its ends. A current of $5.0 \mathrm{~A}$ is set up in the rod through the wires. (a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?(b) What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field the same as before? (Ignore the mass of the wires.) $\mathbf{g}=9.8 \mathrm{~m} \mathrm{~s}^{-2}$ .

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

Length of the rod, I $=0.45 \mathrm{~m}$ Mass suspended, $m=60 \mathrm{~g}=60 \times 10^{-3} \mathrm{Kg}$ Current, $\mid=5 \mathrm{~A}$ (a) Tension in the wire is zero if the magnetic field's force...

A magnetic field set up using Helmholtz coils (described in Exercise $4.16$ ) is uniform in a small region and has a magnitude of $0.75 \mathrm{~T}$ . In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of (single species) charged particles all accelerated through $15 \mathrm{kV}$ enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is $9.0 \times 10^{-5} \mathrm{~V} \mathrm{~m}^{-1}$ , make a simple guess as to what the beam contains. Why is the answer not unique?

CBSE, Class 12, Moving Charges and Magnetism, Physics

Magnetic field, $B=0.75 \mathrm{~T}$ Accelerating voltage, $\mathrm{V}=15 \mathrm{kV}=15 \times 10^{3} \mathrm{~V}$ Electrostatic field, $E=9.0 \times 10^{-5} \mathrm{~V} \mathrm{~m}^{-1}$ Kinetic...

An electron emitted by a heated cathode and accelerated through a potential difference of $2.0 \mathrm{kV}$ , enters a region with a uniform magnetic field of $0.15 \mathrm{~T}$ . Determine the trajectory of the electron if the field (a) is transverse to its initial velocity, (b) makes an angle of $30^{\circ}$ with the initial velocity.

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

Magnetic field, $B=0.15 \mathrm{~T}$ Potential difference, $\mathrm{V}=2.0 \mathrm{kV}$ An electron obtains kinetic energy as a result of $\mathrm{E}=(1 / 2) \mathrm{mv}^{2}$ $\mathrm{eV}=(1 / 2)...

Answer the following questions: (a) A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle? (b) A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?

Class 12, Moving Charges and Magnetism, NCERT, Physics

(a) The force acting on a charged particle, moving in a magnetic field is given by F = q v B sinθ now, if no force acts on the charged particle, it will proceed along a straight path at a constant...

Two moving coil meters, M₁ and M₂ have the following particulars:

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

R1=10Ω, N1=30, A1=3.6×10−3m2,B1=0.25T R2=14Ω,N2=42, A2=1.8×10−3m2,B2=0.5T (The spring constants are identical for the two meters). Determine the ratio of (a) current sensitivity and (b)...

For a circular coil of radius $\mathrm{R}$ and $\mathrm{N}$ turns carrying current $\mathrm{I}$ , the magnitude of the magnetic field at a point on its axis at a distance $x$ from its centre is given by, $B=\frac{\mu_{0} I R^{2} N}{2\left(x^{2}+R^{2}\right)^{3 / 2}}$ (a) Show that this reduces to the familiar result for field at the centre of the coil. (b) Consider two parallel co-axial circular coils of equal radius $\mathbf{R}$ , and number of turns $\mathbf{N}$ , carrying equal currents in the same direction, and separated by a distance $\mathbf{R} .$ Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to $\mathbf{R}$ , and is given by, $B=0.72 \frac{\mu_{0} N I}{R}$ , approximately.

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

(a) Given is the expression of $B$ as $\frac{\mu_{0} I R^{2} N}{2\left(x^{2}+R^{2}\right)^{3 / 2}}$ $x$ will be zero at the centre of the coil, Therefore, the magnetic field at the centre is...

(a) A circular coil having radius as 8.0 cm, number of turn as 30 and carrying a current of 6.0 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field lines make an angle of $60^{o}$ with the normal of the coil. To prevent the coil from turning, determine the magnitude of the counter-torque that must be applied. (b) Would your answer change, if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

(a) Number of turns on the circular coil (n) is given as 30 Radius of the coil (r) is given as 0.08 m Area of the coil: $\pi {r^2}$= $\pi {(0.08)^2}$= $0.0201{m^2}$ Current flowing in the coil (I) =...

A toroid has a core (non-ferromagnetic) of inner radius $25 \mathrm{~cm}$ and outer radius $26 \mathrm{~cm}$ , around which 3500 turns of a wire are wound. If the current in the wire is $11 \mathrm{~A}$ , what is the magnetic field?(a) outside the toroid, (b) inside the core of the toroid

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

The core's inner radius, $r_{1}=0.25 \mathrm{~m}$ The core's outer radius, $r_{2}=0.26 \mathrm{~m}$ The number of wire turns, $N=3500$ turns Current in the wire, $1=11 \mathrm{~A}$ (a) Outside of...

A magnetic field of 100 G is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about ${{10}^{-3}}$ m2. The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound around a core is at most 1000 turns ${{m}^{-1}}$ . Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

Magnetic field strength, B is given as $100 \times {10^{-4}}T$ Number of turns per unit length, N is given as 1000 turns/m Current carrying capacity of the coil is given as 15 A Permeability of free...

Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

Radius of the coil X, r1 is given as 0.16 m Number of turns in coil X, n1 is given as 20 Current in the coil X, I1 is given as 16 A Radius of the coil Y, r2 is given as 0.1 m...

The radionuclide ¹¹C decays according to

CBSE, Class 12, NCERT, Nuclei, Physics

\[{}_{6}^{11}C\to {}_{5}^{11}~B+{{e}^{+}}+v\]: \[{{T}_{\frac{1}{2}}}\] = 20.3 min The maximum energy of the emitted positron is 0.960 MeV.Given the mass values:m (116 C) = 11.011434 u and m...

In a chamber, a uniform magnetic field of 6.5 G is maintained. An electron is shot into the field with a speed of 4.8 x $10^{6}$ m $s^{-1}$ normal to the field. Find the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

Given, Magnetic field strength (B) = 6.5 G = $6.5 \times {10^{ - 4}}T$ Speed of the electron (v) = $4.8 \times {10^6}m/s$ Charge on the electron (e) = $1.6 \times {10^{ - 19}}C$ Mass of the electron...

Find the Q-value and the kinetic energy of the emitted α-particle in the α-decay of

CBSE, Class 12, NCERT, Nuclei, Physics

(a) ${}_{88}^{226}Ra$ (b) ${}_{86}^{222}Rn$ Given m (${}_{88}^{226}Ra$)= 226.02540 u, m (${}_{86}^{222}Rn$) = 222.01750 u, m (${}_{86}^{220}Rn$)= 220.01137 u, m...

In a chamber, a uniform magnetic field of 6.5 G (1 G = $10^{-4}$ T) is maintained. An electron is shot into the field with a speed of $4.8 \times {10^6}m/s$ normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit.

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

Magnetic field strength (B) = 6.5 G = $6.5 \times {10^{ - 4}}T$ Speed of the electron (v) = $4.8 \times {10^6}m/s$ Charge on the electron (e) = $1.6 \times {10^{ - 19}}C$ Mass of the electron (me)...

Obtain approximately the ratio of the nuclear radii of the gold isotope
${}_{79}^{197}Au$
and the
${}_{47}^{107}Ag$
silver isotope .

CBSE, Class 12, NCERT, Nuclei, Physics

Ans: Nuclear radius of the gold isotope \[{}_{79}^{197}Au\]= \[{{R}_{Au}}\] Nuclear radius of the silver isotope \[{}_{47}^{107}Ag\]= \[{{R}_{Ag}}\] Mass number of gold, \[{{A}_{Au}}\]=...

The half-life of is 28 years. What is the disintegration rate of 15 mg of this isotope?

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – Half-life of given by = 28 years Converting into seconds, we get half-life time = 28 × 365 × 24 × 60 × 60 = 8.83 × 108 s Mass of the isotope, m = 15 mg It is implied that...

A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30º with the direction of a uniform
the horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

The length of a square coil's side (l) is 0.1 m. The current flowing through the coil (I) has a magnitude of 12 A. The number of coil turns (n) is 20. The angle formed by the coil's plane with B...

Obtain the amount of
${}_{27}^{60}Co$
necessary to provide a radioactive source
of 8.0 mCi strength. The half-life of
${}_{27}^{60}Co$
is 5.3 years.

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – We are given the strength of the radioactive source as – \[\frac{dN}{dt}=8.0mCi\] = 8 x 10-3 x 3.7 x 1010 = 29.6 x 107 decay/s Where, N is the required number of atoms Half-life...

A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

The length of the solenoid (l) is 80 cm (0.8 m). On the solenoid, there are five levels of windings, each with 400 turns. ∴ Total number of solenoid rotations, N = 5 x 400 = 2000 Diameter of the...

The normal activity of living carbon-containing matter is found to be about 15 decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive
${}_{6}^{14}C$
present with the stable carbon isotope
${}_{6}^{12}C$
. When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life (5730 years) of
${}_{6}^{14}C$
, and the measured activity, the age of the specimen can be approximately estimated. This is the principle of
${}_{6}^{14}C$
dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus-Valley civilisation.

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – We are given the decay rate of living carbon-containing matter, R = 15 decay/min Let N represent the number of radioactive atoms present in a normal carbon-containing matter. Half- life...

A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to a) 3.125%, b) 1% of its original value?

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – It is given that the half-life of the given radioactive isotope is T years Let N0 represent the initial amount of radioactive isotope. (a) After...

Write nuclear reaction equations for

CBSE, Class 12, NCERT, Nuclei, Physics

α-decay of ${}_{88}^{226}Ra$α-decay of ${}_{94}^{224}Pu$β−-decay of \[{}_{15}^{32}P\] β– -decay of \[{}_{83}^{210}B\]β+-decay of \[{}_{6}^{11}C\] β+ -decay of...

Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

The magnitude of the current flowing in the wire $A({I_A})$ is 8 A The magnitude of the current flowing in wire $B({I_B})$ is 5 A The distance between the two wires (r) is 0.04 m The length of the...

A given coin has a mass of 3.0 g. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity assume that the coin is entirely made of
${}_{29}^{63}Cu$
with mass = 62.92960 u.

CBSE, Class 12, NCERT, Nuclei, Physics

Answer...

A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

The wire's length (l) is 3 cm or 0.03 m The current running through it (I) is 10 A. The magnetic field strength (B) is 0.27 T. the angle formed by the current and the magnetic field is $\theta ...

Obtain the binding energy of the nuclei
${}_{26}^{56}Fe$
and
${}_{83}^{209}Bi$
in units of MeV from the following

CBSE, Class 12, NCERT, Nuclei, Physics

data: m (\[{}_{26}^{56}Fe\]) = 55.934939 u m(\[{}_{83}^{209}Bi\]) = 208.980388 u We are given that, Atomic mass of \[{}_{26}^{56}Fe\] is m1 = 55.934939 u We know that \[{}_{26}^{56}Fe\] nucleus...

What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30º with the direction of a uniform magnetic field of 0.15 T?

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

The current going through the wire (I) is 8 A. The uniform magnetic field (B) has a magnitude of 0.15 T. The angle between the wire and the magnetic field is $\theta = {30^ \circ }$ We...

Obtain the binding energy in MeV of a nitrogen nucleus
${}_{7}^{14}N$
, given m
${}_{7}^{14}N$
=14.00307 u

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – Atomic mass of nitrogen \[{}_{7}^{14}N\], m = 14.00307 u We know that a nucleus of \[{}_{7}^{14}N\] nitrogen contains 7 neutrons and 7 protons. So – The defect mass formula is...

A horizontal overhead power line carries a current of 90 A in the east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

(I) = 90 A is the magnitude of the current in the power line. The point is placed at (r) = 1.5 m below the electrical cable. As a result, the magnetic field at that location may be computed as...

The three stable isotopes of neon:
${}_{10}^{20}Ne$
,
${}_{10}^{21}Ne$
and
${}_{10}^{22}Ne$
have respective abundances of 90.51%, 0.27% and 9.22%. The atomic masses of the three isotopes are 19.99 u, 20.99 u and 21.99 u, respectively. Obtain the average atomic mass of neon.

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – We are given, Mass of neon isotope - \[{}_{10}^{20}Ne\], m1 = 19.99 u Abundance of neon isotope - \[{}_{10}^{20}Ne\], n1 = 90.51% Mass of neon isotope - \[{}_{10}^{21}Ne\],...

(a) Lithium has two stable isotopes
${}_{3}^{6}Li$
and
${}_{3}^{7}Li$
have respective abundances of 7.5% and 92.5%. These isotopes have masses 6.01512 u and 7.01600 u, respectively. Find the atomic mass of lithium. (b) Boron has two stable isotopes, _{5}^{10}{B}510B and _{5}^{11}{B}511B . Their respective masses are 10.01294 u and 11.00931 u, and the atomic mass of boron is 10.811 u. Find the abundances of ${}_{5}^{10}B$ and ${}_{5}^{11}B$ .

CBSE, Class 12, Guides, NCERT, Nuclei, Physics

Answer – We are given, Mass of lithium isotope - \[{}_{3}^{6}Li\], m1 = 6.01512 u Mass of lithium isotope - \[{}_{3}^{7}Li\], m2 = 7.01600 u We are also given their abundances, so –...

A long straight wire in the horizontal plane carries a current of 50 A in the north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.

CBSE, Class 12, Moving Charges and Magnetism, NCERT, Physics

The current flowing across the wire has a magnitude of (I) = 50 A. The point B is 2.5 metres east of the wire. As a result, the magnitude of the point's distance from the wire (r) is 2.5 m. The...

A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?

CBSE, Class 12, Moving Charges and Magnetism, Physics, Physics

The current flowing through the wire (I) has a magnitude of 35 A. The point's distance from the wire (r) is 20 cm (0.2 m). The magnitude of the magnetic field is given at this position by the...

Obtain the first Bohr’s radius and the ground state energy of a muonic hydrogen atom [i.e., an atom in which a negatively charged muon (μ−) of mass about 207me orbits around a proton].

Atoms, CBSE, Class 12, NCERT, Physics

Answer – We are given that the mass of a negatively charged muon is mμ = 207 me Now, According to Bohr’s model bohr’s radius is given by – \[{{r}_{e}}\alpha \left( \frac{1}{{{m}_{e}}}...

If Bohr’s quantization postulate (angular momentum = nh/2π) is a basic law of nature, it should be equally valid for the case of planetary motion as well. Why then do we never speak of quantization of orbits of planets around the sun?

Atoms, CBSE, Class 12, NCERT, Physics

Answer – The quantum level for a planetary motion is taken to be continuous. This can be explained by the fact that the planetary motion’s angular momentum is largely relative to the value of...

The total energy of an electron in the first excited state of the hydrogen atom is about –3.4 eV.
(a) What is the kinetic energy of the electron in this state?
(b) What is the potential energy of the electron in this state?
(c) Which of the answers above would change if the choice of the zero of potential energy is changed?

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – (a) Total energy of the electron is given by E = – 3.4 eV We know that the kinetic energy of the electron is equal to the negative of the total energy. So, K.E = – E K.E = – (- 3.4 ) = +...

Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (~ 10^–10m).
(a) Construct a quantity with the dimensions of length from the fundamental constants e, m_e, and c. Determine its numerical value.
(b) You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in a non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr discard c and look for ‘something else’ to get the right atomic size. Now, the Planck’s constant h had already made its appearance elsewhere. Bohr’s great insight lay in recognising that h, m_e, and e will yield the right atomic size. Construct a quantity with the dimension of length from h, m_e, and e and confirm that its numerical value has indeed the correct order of magnitude.

CBSE, Class 12, NCERT, Nuclei, Physics

Ans: (a) We are given, The charge on an electron, e = 1.6 x 10-19 C Mass of an electron, me = 9.1 x 10-31 kg Speed of the light, c = 3 x 108 m/s The equation comprising of above...

Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n–1). For large n, show that this frequency equals the classical frequency of revolution of the electron in the orbit.

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – We are given that the hydrogen atom de-excites from the level n to level (n-1). Now, writing the equation for energy (E1) of the radiation for the level n. we have –...

The gravitational attraction amongst proton and electron in a hydrogen atom is weaker than the coulomb attraction by a component of around 10−40. Another option method for taking a gander at this case is to assess the span of the first Bohr circle of a hydrogen particle if the electron and proton were bound by gravitational attraction. You will discover the appropriate response fascinating.

CBSE, Class 12, NCERT, Nuclei, Physics

Answer...

Choose a suitable solution to the given statements which justify the difference between Thomson’s model and Rutherford’s model

CBSE, Class 12, NCERT, Nuclei, Physics

(a) In the case of scattering of alpha particles by a gold foil, average angle of deflection of alpha particles stated by Rutherford’s model is (less than, almost the same as, much greater than)...

In accordance with the Bohr’s model, find the quantum number that characterizes the earth’s revolution around the sun in an orbit of radius 3 × 1011 m with orbital speed 3 × 104 m/s. (Mass of earth = 6.0 × 1024 kg.)

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – We know that the radius of the Earth’s orbit around the Sun is given by r = 1.5 × 1011 m We are given the orbital speed of the Earth, ν = 3 × 104 m/s Also, the mass of the Earth,...

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – It has been given that 12.5 eV is the energy of the electron beam used to bombard gaseous hydrogen at room temperature. Also, −13.6 eV is the ground state energy of the gaseous...

The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – We are given the radius of the innermost orbit of a hydrogen atom as r1 = 5.3 × 10−11 m. Suppose r2 represents the radius of the...

(a) Using the Bohr’s model, calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbital period in each of these levels.

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – Let the orbital speed of the electron in the ground state level of an hydrogen atom, n1= 1, be given by v1 . For charge (e) of an electron, v1 is given by the relation –...

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.

CBSE, Class 12, NCERT, Nuclei, Physics

Answer – We know that for ground level, n1 = 1 Suppose E1 is the energy of the level n1. So as we know E1 is related with n1 as – \[{{E}_{1}}=\frac{13.6}{{{n}_{1}}^{2}}eV=-13.6eV\]...

The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state?

CBSE, Class 12, NCERT, Nuclei, Physics

We know that the ground state energy of hydrogen atom is given by – E = − 13.6 eV The total energy of hydrogen atom is equal to -13.6 eV. It is understood that the kinetic energy is equal to the...

A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom make a transition from the upper level to the lower level?

CBSE, Class 12, Guides, NCERT, Nuclei, Physics

Answer – We know that the separation of two energy levels in an atom is given by the relation – \[E=2.3eV=2.3\times 1.6\times {{10}^{-19}}\] \[E=3.68\times {{10}^{-19}}J\] Let v be the frequency of...

What is the shortest wavelength present in the Paschen series of spectral lines?

CBSE, Class 12, Guides, NCERT, Nuclei, Physics

Answer – Using the Rydberg’s formula, given the relation – \[\frac{hc}{\lambda }=21.76\times {{10}^{-19}}[\frac{1}{{{n}_{1}}^{2}}-\frac{1}{{{n}_{2}}^{2}}]\] Where h is the Planck’s constant, given =...

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

CBSE, Class 12, Guides, NCERT, Nuclei, Physics

Answer – It is quite known that the mass of the incident alpha particle (6.64 × 10-27kg) is much more than the mass of hydrogen (1.67 × 10-27Kg). Hence, the alpha particle would fail to rebound...

Choose the correct alternative from the clues given at the end of each statement:

CBSE, Class 12, NCERT, Nuclei, Physics

(a) In Rutherford’s model the atomic size is ……….. the size of the atom in Thomson’s model. (much greater than/no different from/much less than.) (b) ) In ………. the ground state electrons...

Is it necessary for a transmitting antenna to be at the same height as that of the receiving antenna for line-of-sight communication? A TV transmitting antenna is 81 m tall. How much service area can it cover if the receiving antenna is at the ground level?

CBSE, Class 12, Communication Systems, Guides, NCERT, Physics

Answer – \[3256k{{m}^{2}}\] There is no physical obstruction between the transmitter and the receiver antennae in case of the line-of-sight communication and hence there is no such requirement that...

Due to economic reasons, only the upper sideband of an AM wave is transmitted, but at the receiving station, there is a facility for generating the carrier. Show that if a device is available which can multiply two signals, then it is possible to recover the modulating signal at the receiver station.

CBSE, Class 12, Communication Systems, Guides, NCERT, Physics

Answer – Let the carrier wave frequency be represented by \[{{\omega }_{c}}\] and let \[{{\omega }_{s}}\]be the signal wave frequency. Then the received signal will be given by...

For an amplitude modulated wave, the maximum amplitude is found to be 10V while the minimum amplitude is found to be 2V. Determine the modulation index, µ. What would be the value of µ if the minimum amplitude is zero volts?

CBSE, Class 12, Communication Systems, Guides, NCERT, Physics

Answer – According to the question, we have – Maximum Amplitude; \[{{A}_{max~}}\] = 10 V Minimum Amplitude; \[{{A}_{min}}~\]= 2 V It is quite known that the modulation index of an amplitude...

A carrier wave of peak voltage 12 V is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of 75%?

CBSE, Class 12, Communication Systems, Guides, NCERT, Physics

Answer – 9V Explanation – We are given – Amplitude of carrier wave ; \[{{A}_{c}}\] = 12 V Modulation index (m) = 75% = 0.75 Amplitude of the modulating wave = ${{A}_{m}}$ We will now use the...

Digital signals

CBSE, Class 12, Communication Systems, NCERT, Physics

(i) Do not provide a continuous set of values (ii) Represent value as discrete steps (iii) Can utilize binary system (iv) Can utilize decimal as well as binary systems State which statement(s) are...

Frequencies in the UHF range normally propagate by means of :

CBSE, Class 12, Communication Systems, NCERT, Physics

(1) Ground Waves (2) Sky Waves (3) Surface Waves (4) Space Waves ANSWER – Space Waves Explanation – An ultra-high frequency (UHF) wave cannot be reflected back by the ionosphere as the highly...

Which of the following frequencies will be suitable for beyond-the horizon communication using sky waves?

CBSE, Class 12, Communication Systems, Guides, NCERT, Physics

(1) 10 kHz (2) 10 MHz (3) 1 GHz (4) 1000 GHz Answer - 10 MHz In case of beyond – the – horizon communication, the signal needs to cover large distances. For a signal of frequency 10kHz, the signal...

Suppose that the particle in Exercise $1.33$ is an electron projected with velocity $\mathrm{v}_{\mathrm{x}}=\mathbf{2 . 0} \times 10^{6} \mathrm{~m}$ $\mathrm{s}^{-1}$ . If E between the plates separated by $0.5 \mathrm{~cm}$ is $9.1 \times 10^{2} \mathrm{~N} / \mathrm{C}$ , where will the electron strike the upper plate? $\left(|\mathrm{e}|=1.6 \times 10^{-19} \mathrm{C}, \mathrm{m}_{\mathrm{e}}=9.1 \times 10^{-31} \mathrm{~kg}_{-}\right)$

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: Given: Velocity of the electron, $\mathrm{v}_{\mathrm{x}}=2.0 \times 10^{6} \mathrm{~m} \mathrm{~s}^{-1}$ Separation between the plates, $d=0.5 \mathrm{~cm}=0.5 \times 10^{-2} \mathrm{~m}$...

a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart. Solution: a) Assume that the equilibrium is at a state of stability....

It is now established that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called ‘up’ quark (denoted by u) of charge + (2/3) e, and the ‘down’ quark (denoted by d) of charge (–1/3) e, together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron.

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: Given, the net charge of a proton is +e. The value +e can be got when $p=\left(\frac{2}{3}+\frac{2}{3}-\frac{1}{3}\right) e$ The net charge of a neutron is 0 . This can be got when...

Obtain the formula for the electric field due to a long thin wire of uniform linear charge density E without using Gauss’s law. [Hint: Use Coulomb’s law directly and evaluate the necessary integral.]

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution:Consider the case of a long thin wire with a uniform linear charge density of 0 to 1. At r from the middle C of the wire, a point P is marked on the wire. The electric field produced by the...

A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is $\frac{\sigma}{2 \epsilon_{0}} \hat{n}$ , where $\mathrm{n}^{\hat{ }}$ is the unit vector in the outward normal direction and $\sigma$ is the surface charge density near the hole.

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: If we assume that the hole has been filled, then Gauss's formula may be used to calculate the electric field intensity at a location near to the surface of the conductor, where Flux,...

(a) A conductor A with a cavity as shown in Fig. (a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor. (b) Another conductor B with charge q is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q + q [Fig. (b)]. (c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: (a) Within the conductor that encloses the hollow, a Gaussian surface is taken into consideration. Within the conductor, the electric field strength (E) will be 0, indicating that it is...

In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 105 NC–1 per metre. What are the force and torque experienced by a system having a total dipole moment equal to 10–7 cm in the negative z-direction?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Answer: Total dipole moment of the system, p=q×dl=−10−7 cm The rate of increase of the magnitude of the electric field along the positive z-direction = 105 NC–1 per metre. The...

Which among the curves shown in Fig. cannot possibly represent electrostatic field lines?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution:a. In the first case, the field lines are not parallel to the conductor's surface. As a result, it does not correspond to electrostatic field lines at...

An oil drop of 12 excess electrons is held stationary under a constant electric field of $2.55 \times$ $10^{4} \mathrm{NC}^{-1}$ (Millikan’s oil drop experiment). The density of the oil is $1.26 \mathrm{~g} \mathrm{~cm}^{-3} .$ Estimate the radius of the drop.
$\left(g=9.81 \mathrm{~m} \mathrm{~s}^{-2} ; \mathrm{e}=1.60 \times 10^{-19} \mathrm{C}\right)$

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: Given: Excess electron on an oil drop, $n=12$ Electric field intensity, $E=2.55 \times 10^{4} \mathrm{NC}^{-1}$ Density of oil, $\rho=1.26 \mathrm{~g} \mathrm{~cm}^{-3}$ Acceleration due...

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude $17.0 \times 10^{-22} \mathrm{C} / \mathrm{m}^{2}$

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

What is E: (a) In the outer region of the first plate, (b) In the outer region of the second plate, and ( c) between the plates? Solution: As seen in the accompanying illustration, the scenario...

An infinite line charge produces a field of $9 \times 10^{4} \mathrm{~N} / \mathrm{C}$ at a distance of $2 \mathrm{~cm} .$ Calculate the linear charge density.

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: The electric field produced by infinite line charges at a distance $d$ with linear charge density $\lambda$ is given by the relation, where is the distance in metres. $E=\frac{\lambda}{2...

A uniformly charged conducting sphere of $2.4 \mathrm{~m}$ diameter has a surface charge density of $80.0$ $\mu \mathrm{C} / \mathrm{m}^{2}$

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

(a) Find the charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere? Solution: (a) Given: The diameter of the sphere, $d=2.4 \mathrm{~m}$ The radius of the...

A conducting sphere of radius $10 \mathrm{~cm}$ has an unknown charge. If the electric field $20 \mathrm{~cm}$ from the centre of the sphere is $1.5 \times 10^{3} \mathrm{~N} / \mathrm{C}$ and points radially inward, what is the net charge on the sphere?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: The strength of the electric field ( $E$ ) at a distance ( $d$ ) from the centre of a sphere holding net charge ( $q$ ) may be calculated using the following relationship: $E=\frac{1}{4...

A point charge causes an electric flux of $-1.0 \times 10^{3} \mathrm{~N} \mathrm{~m}^{2} / \mathrm{C}$ to pass through a spherical Gaussian surface of $10.0 \mathrm{~cm}$ radius centred on the charge.

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

(a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is the value of the point charge? Solution: (a)Given: Electric flux, $\Phi=-1.0 \times...

A point charge $+10 \mu \mathrm{C}$ is at a distance $5 \mathrm{~cm}$ directly above the centre of a square of side $10 \mathrm{~cm}$ , as shown in Fig. 1.34. What is the magnitude of the electric flux through the square?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

( Hint : Think of the square as one face of a cube with edge $10 \mathrm{~cm}$ ) Solution:One way to think of the square is as one of the faces of a cube with an edge and a centre where the charge...

Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is $8.0 \times 10^{3} \mathrm{~N} \mathrm{~m}^{2} / \mathrm{C}$ .
(a) What is the net charge inside the box?
(b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or Why not?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solutions: (a)Given: Net outward flux through the surface of the box, $\varphi=8.0 \times 10^{3} \mathrm{~N} \mathrm{~m}^{2} / \mathrm{C}$ Concept: For a body containing net charge $q$, flux...

What is the net flux of the uniform electric field of Exercise $1.15$ through a cube of side $20 \mathrm{~cm}$ oriented so that its faces are parallel to the coordinate planes?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: The faces of a cube are all parallel to the coordinate axes on both sides of the object. So the number of field lines entering the cube is equal to the number of field lines piercing...

Consider a uniform electric field $\mathrm{E}=\mathbf{3} \times \mathbf{1 0}^{3} \hat{\mathrm{i}} \mathrm{N} / \mathrm{C}$ .

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

(a) What is the flux of this field through a square of $10 \mathrm{~cm}$ on a side whose plane is parallel to the y $z$ - plane? (b) What is the flux through the same square if the normal to its...

The figure below shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to the mass ratio?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

We can see that particles 1 and 2 are traveling in the direction of the positive charge, and we know that opposing charges attract and identical charges repel. As a result, we may say that the...

Suppose the spheres A and B in Exercise 12 have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between $\mathbf{A}$ and $\mathbf{B}$ ?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: Given: Distance between the spheres, $A$ and $B, r=0.5 \mathrm{~m}$ Initially, the charge on each of sphere $q=6.5 \times 10^{-7} C$ Concept and Calculation: When the sphere is contacted...

(i) Two insulated charged copper spheres A and B have their centers separated by a distance of $50 \mathrm{~cm}$ . What is the mutual force of electrostatic repulsion if the charge on each is $6.5$ $\times 10^{-7} \mathrm{C}$ each? The radii of $\mathbf{A}$ and $\mathrm{B}$ are negligible compared to the distance of separation.
(ii) What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: i) Given: Charge on sphere $\mathrm{A}, q_{A}=6.5 \times 10^{-7} C$ Charge on sphere $\mathrm{B}, q_{B}=6.5 \times 10^{-7} \mathrm{C}$ Distance between the spheres, $r=50 \mathrm{~cm}=0.5...

A polythene piece rubbed with wool is found to have a negative charge of $3 \times 10^{-7} \mathrm{C} .$
(i) Estimate the number of electrons transferred (from which to which?)
(ii) Is there a transfer of mass from wool to polythene?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: (i) Because the wool is positively charged and the polythene is negatively charged, we can state that only a small number of electrons are transported from wool to polythene during the...

An electric dipole with dipole moment $4 \times 10^{-9} C \mathrm{Cm}$ is aligned at $30^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^{4} N C^{-1} .$ Calculate the magnitude of the torque acting on the dipole.

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: Given: Electric dipole moment, $p=4 \times 10^{-9} C m$ Angle made by $p$ with a uniform electric field, $\theta=30^{\circ}$ Electric field, $E=5 \times 10^{4} N C^{-1}$ Concept: Torque...

A system has two charges $q_{A}=2.5 \times 10^{-7} C$ and $q_{B}=-2.5 \times 10^{-7} C$ located at points $A:(0,0,-15 \mathrm{~cm})$ and $B(0,0,+15 \mathrm{~cm})$ , respectively. What is the total charge and electric dipole moment of the system?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: Given: The charges which are located at the given points are shown in the co-ordinate system as At point $\mathrm{A}$, charge, $q_{A}=2.5 \times 10^{-7} C$ At point $B$, charge,...

Two-point charges qA = 3 µC and qB= –3 µC are located 20 cm apart in a vacuum.
(i) What is the electric field at the midpoint O of the line AB joining the two charges?
(ii) If a negative test charge of magnitude 1.5 × ${10^{ - 9}}$ C is placed at this point, what is the force experienced by the test charge?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

i) Given: Charges: qA = 3 µC qB= –3 µC Distance between them = 20 cm Diagrammatic representation of the above question is: Concept: An electric field is a physical field that surrounds...

i) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

(ii) Explain why two field lines never cross each other at any point. Answer: i) It is true that when a charge is placed in an electrostatic field, it will experience a constant force. As a result,...

Four-point charges $q_{A}=2 \mu C, q_{B}=-5 \mu C, q_{C}=2 \mu C, a n d q_{D}=-5 \mu C$ are located at the corners of a square $A B C D$ of side $10 \mathrm{~cm}$ . What is the force on a charge of $1 \mu C$ placed at the center of the square?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: The square that was described in the inquiry is seen in the illustration above. Four charges are put in the corners of the squares on each side of the squares with a 10 cm side. And the...

When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Answer: Whenever two bodies are rubbed against one other, a charge develops on both of the bodies involved. These charges are identical in magnitude but diametrically opposed in type. Charging by...

(i) Explain the meaning of the statement ‘electric charge of a body is quantized’.

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

(ii) Why can one ignore quantization of electric charge when dealing with macroscopic i.e., large-scale charges? Solution i) "It is quantized" in the sense that only integral (1,2,…. n) numbers of...

Check that the ratio $\mathrm{ke}^{2} / \mathbf{G} \mathbf{m}_{\mathrm{e}} \mathrm{m}_{\mathrm{p}}$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: We know that the ratio to be determined is given as follows: $\frac{k e^{2}}{G m_{e} m_{p}}$ where $G$ is the gravitational constant in $N \mathrm{~m}^{2} \mathrm{~kg}^{-2}$ $m_{e}$ and...

The electrostatic force on a small sphere of charge $0.4 \mu \mathrm{C}$ due to another small sphere of charge $-0.8 \mu \mathrm{C}$ in the air is $0.2 \mathrm{~N}$ .
(a) What is the distance between the two spheres?
(b) What is the force on the second sphere due to the first?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: a. Given: The charge on $1^{\text {st }}$ sphere $\left(q_{1}\right)$ and $2^{\text {nd }}$ sphere $\left(q_{2}\right)$ is $0.4 \mu C$ or $0.4 \times 10^{-6} C$ and $-0.8 \times 10^{-6}...

What is the force between two small charged spheres having charges of $2 \times 10^{-7} \mathrm{C}$ and $3 \mathrm{x}$ $10^{-7}$ C placed $30 \mathrm{~cm}$ apart in the air?

CBSE, Class 12, Electric Charges and Fields, NCERT, Physics

Solution: Given: The Charge on the $1^{\text {st }}$ sphere, $q_{1}=2 \times 10^{-7} \mathrm{C}$ The Charge on the $2^{\text {nd }}$ sphere, $q_{2}=3 \times 10^{-7} \mathrm{C}$ The distance...