NCERT Exemplar

A long straight cable of length I is placed symmetrically along the z-axis and has radius a. The cable consists of a thin wire and a co-axial conducting tube. An alternating current I(t)=I_{0} sin (2\pi vt) flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance s from the wire inside the cable is \mathbf{E}(\mathrm{s}, \mathrm{t})=\mu_{0} \mathrm{l}_{0} \mathrm{~V} cos (2\pi vt). In \left(\frac{s}{a}\right) \hat{k},
a) calculate the displacement current density inside the cable
b) integrate the displacement current density across the cross-section of the cable to find the total displacement current I

a) The displacement current density is given as $\vec{J}_{d}=\frac{2 \pi I_{0}}{\lambda^{2}} \ln \frac{a}{s} \sin 2 \pi v t \hat{k}$ b) Total displacement current will be, $I^{d}=\int J_{d} 2 \pi s...

read more

What happens to the intensity of light from a bulb if the distance from the bulb is doubled? As a laser beam travels across the length of a room, its intensity essentially remains constant. What geometrical characteristics of the LASER beam is responsible for the constant intensity which is missing in the case of light from the bulb?

When the distance between two points is doubled, the intensity of light is reduced by one-fourth. Geometrical characteristics of the LASER are: a) unidirectional b) monochromatic c) coherent...

read more

Electromagnetic waves with wavelength
i) \lambda_{1} is used in satellite communication
ii) \lambda_{2} is used to kill germs in water purifies
iii) \lambda_{3} is used to detect leakage of oil in underground pipelines
iv) \lambda_{4} is used to improve visibility in runaways during fog and mist conditions
a) identify and name the part of the electromagnetic spectrum to which these radiations belong
b) arrange these wavelengths in ascending order of their magnitude
c) write one more application of each

a) i) $\lambda_{1}$ is a microwave, used in satellite communication. ii) $\lambda_{2}$ is UV rays, used in a water purifier for killing germs. iii) $\lambda_{3}$ is X-rays, used in improving the...

read more

Consider a light beam incident from air to a glass slab at Brewster’s angle as shown in the figure.A polaroid is placed in the path of the emergent ray at point P and rotated about an axis passing through the centre and perpendicular to the plane of the polaroid (a) For a particular orientation, there shall be darkness as observed through the polaroid (b) The intensity of light as seen through the polaroid shall be independent of the rotation (c) The intensity of light as seen through the Polaroid shall go through a minimum but not zero for two orientations of the polaroid (d) The intensity of light as seen through the polaroid shall go through a minimum for four orientations of the polaroid

The correct answer is c) The intensity of light as seen through the Polaroid shall go through a minimum but not zero for two orientations of the polaroid

read more

In a Young’s double-slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case (a) there shall be alternate interference patterns of red and blue (b) there shall be an interference pattern for red distinct from that for blue (c) there shall be no interference fringes (d) there shall be an interference pattern for red mixing with one for blue

The correct answer is c) there shall be no interference fringes

read more

Two sources S1 and S2 of intensity I 1 and I 2 are placed in front of a screen in the figure (a). The pattern of intensity distribution seen in the central portion is given by the figure (b). In this case which of the following statements are true;(a) S1 and S2 have the same intensities (b) S1 and S2 have a constant phase difference (c) S1 and S2 have the same phase (d) S1 and S2 have the same wavelength.

The correct answer is a) S1 and S2 have the same intensities b) S1 and S2 have a constant phase difference c) S1 and S2 have the same phase

read more

(i) In the explanation of the photoelectric effect, we assume one photon of frequency ν collides with an electron and transfers its energy. This leads to the equation for the maximum energy Emax of the emitted electron as Emax = hν – φ0 where φ0 is the work function of the metal. If an electron absorbs 2 photons (each of frequency ν ) what will be the maximum energy for the emitted electron? (ii) Why is this fact (two-photon absorption) not taken into consideration in our discussion of the stopping potential?

i)According to the question, the electron absorbs two protons with frequencies of v and v'= 2v, where v' is the frequency of the released electron. Emax = hv – ϕ0 ii) There is no emission since the...

read more

Consider a beam of electrons (each electron with energy E0) incident on a metal surface kept in an evacuated chamber. Then (a) no electrons will be emitted as only photons can emit electrons (b) electrons can be emitted but all with an energy, E0 (c) electrons can be emitted with any energy, with a maximum of E0 – φ (φ is the work function) (d) electrons can be emitted with any energy, with a maximum of E0

The correct answer is d) electrons can be emitted with any energy, with a maximum of E0

read more

An electromagnetic wave travels in vacuum along z-direction: E=\left(E_{1} \hat{i}+E_{2} \hat{j}\right) \cos (k z-\omega t) \cdot Choose the correct options from the following:
a) the associated magnetic field is given as B=\frac{1}{c}\left(E_{1} \hat{i}-E_{2} \hat{j}\right) \cos (k z-\omega t)
b) the associated magnetic field is given as B=\frac{1}{c}\left(E_{1} \hat{i}-E_{2} \hat{j}\right) \cos (k z-\omega t)
c) the given electromagnetic field is circularly polarised
d) the given electromagnetic waves is plane polarised

a) the associated magnetic field is given as $B=\frac{1}{c}\left(E_{1} \hat{i}-E_{2} \hat{j}\right) \cos (k z-\omega t)$ d) the given electromagnetic waves is plane polarised

read more

For an LCR circuit driven at frequency ω, the equation reads L di/dt + Ri + q/C = vi = vm sin ꞷ t
(i) Cast the equation in the form of a conservation of energy statement
(ii) Integrate the equation over one cycle to find that the phase difference between v and i must be acute.

i) The first equation is in the form of conservation of energy ii) We get dt as positive when we integrate the equation from $0$ to $T$, which is possible when the phase difference is constant and...

read more

An electrical device draws 2kW power from AC mains (voltage 223V (rms) = 50,000 V). The current differs (lags) in phase by φ (tan φ = -3/4) as compared to voltage.
Find (i) R,
(ii) X_{c}-X_{l},
and (iii) I_{M}. Another device has twice the values for R, X_{C} and X_{L}. How are the answers affected?

Impedance is given as Z = 25 ohms $635=25R^{2}/16$ a) Resistance can be calculated as, $R=\sqrt 25\times 16=\sqrt 400=20 ohms$ b) $X_{c}-X_{l}=-3R/4=-15ohms$ c) Main current will be...

read more

A device ‘X’ is connected to an a.c source. The variation of voltage, current and power in one complete cycle is shown in the figure.
(a) Which curve shows power consumption over a full cycle?
(b) What is the average power consumption over a cycle?

Solution: a) The greatest amplitude of the power curve is equal to the product of the voltage and current amplitudes. As a result, curve A denotes power. b) Because the whole cycle in the graph...

read more

For an LCR circuit, the power transferred from the driving source to the driven oscillator is P = I2Z cos φ.
(a) Here, the power factor cos 0, 0. φ ≥ ≥ P
(b) The driving force can give no energy to the oscillator (P = 0) in some cases.
(c) The driving force cannot syphon out (P < 0) the energy out of oscillator.
(d) The driving force can take away energy out of the oscillator.

The correct options are: (a) Here, the power factor cos 0, 0. φ ≥ ≥ P (b) The driving force can give no energy to the oscillator (P = 0) in some cases. (c) The driving force cannot syphon out (P...

read more

(a) Explain the following phenomena with the help of Henry’s law. (i) A painful condition known as bends. (ii) Feeling of weakness and discomfort in breathing at high altitude. (b) Why soda water bottle kept at room temperature fizzes on opening?

(a) (i)  The bend is a condition that occurs in scuba divers. They have to breathe air under high pressure under water. Nitrogen gas does not dissolve in normal pressure. Under water, they will...

read more

Components of a binary mixture of two liquids A and B were being separated by distillation. After some time separation of components stopped and the composition of the vapour phase became the same as that of a liquid phase. Both the components started coming in the distillate. Explain why this happened.

An azeotropic mixture is shown when both the liquids A & B starts coming in the distillate and the vapour and liquid phase will have the same composition. Via distillation an azeotropic mixture...

read more

Two beakers of capacity 500 mL were taken. One of these beakers, labeled as “A”, was filled with 400 mL water whereas the beaker labelled “B” was filled with 400 mL of 2 M solution of NaCl. At the same temperature, both the beakers were placed in closed containers of the same material and same capacity as shown in Figure. At a given temperature, which of the following statement is correct about the vapour pressure of pure water and that of NaCl solution.

(i) the vapour pressure in container (A) is more than that in a container (B). (ii) the vapour pressure in container (A) is less than that in the container (B). (iii) vapour pressure is equal in...

read more

A multirange current meter can be constructed by using a galvanometer circuit shown in the figure. We want a current meter that can measure 10 mA, 100 mA, and 1 A using a galvanometer of resistance 10Ω and that produces maximum deflection for a current of 1 mA. Find S1, S2, and S3 that have to be used.

I1 is measured as = 10 mA = IGG = (I1 – IG)(S1 + S2 + S3) I2 is measured as = 100 mA = IG(G+S1)=(I2-IG)(S2-S3) I3 is measured as = 1 A = IG(G+S1+S2)=(I3-IG)(S3) S1 = 1 Ω S2 = 0.1 Ω S3 = 0.01...

read more

Consider a circular current-carrying loop of radius R in the x-y plane with centre at the origin. Consider the line integral\Im (L)=\left| \left. \int_{-L}^{L}{B.dl} \right| \right.a) show that\Im (L)monotonically increases with L b) use an appropriate Amperian loop to that\Im (\infty )={{\mu }_{0}}Iwhere I is the current in the wire c) verify directly the above result d) suppose we replace the circular coil by a square coil of sides R carrying the same current I. What can you say about\Im (\infty )\text{and }\Im \text{(L)}

a) A circular current-carrying loop's magnetic field is given as \(\Im (L)=\int_{-L}^{+L}{Bdl}=2Bl\) It is a L function that increases monotonically. b) The Amperian loop is defined as follows:...

read more

A current-carrying loop consists of 3 identical quarter circles of radius R, lying in the positive quadrants of the x-y, y-z, and z-x planes with their centres at the origin, joined together. Find the direction and magnitude of B at the origin.

The quarter's vector sum of the magnetic field at the origin is given as \({{\vec{B}}_{net}}=\frac{1}{4}\left( \frac{{{\mu }_{0}}I}{2R} \right)(\widehat{i}+\widehat{j}+\widehat{k})\)

read more