NCERT

Figure below shows a 2.0 V potentiometer used for the determination of internal resistance of a 1.5 V cell. The balance point of the cell in open circuit is 76.3 cm. When a resistor of 9.5 Ω is used in the external circuit of the cell, the balance point shifts to 64.8 cm length of the potentiometer wire. Determine the internal resistance of the cell.

Answer – According to the question statement – Internal resistance of the cell is r = 1.5 V cell Balance point of the cell in open circuit is l = 76.3 cm External resistance is R = 9.5 Ω...

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Figure shows a potentiometer with a cell of 2.0 V and internal resistance 0.40 Ω maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02 V (for very moderate currents upto a few mA) gives a balance point at 67.3 cm length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of 600 kΩ is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf ε and the balance point found similarly, turns out to be at 82.3 cm length of the wire.

(a) What is the value ε?  (b) What purpose does the high resistance of 600 kΩ have? (c) Is the balance point affected by this high resistance  (d) Would the method work in the above...

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(a) Given n resistors each of resistance R, how will you combine them to get the (i) maximum (ii) minimum effective resistance? What is the ratio of the maximum to minimum resistance?
(b) Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of (i) (11/3) Ω (ii) (11/5) Ω, (iii) 6Ω, (iv) (6/11) Ω?
(c) Determine the equivalent resistance of networks shown in figure

Answer – (a) The total number of resistors is equal to n. Each resistor's resistance is equal to R.  (i) When the resistors are connected in series, the maximum effective resistance is...

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Choose the correct alternative:
(a) Alloys of metals usually have (greater/less) resistivity than that of their constituent metals.
(b) Alloys usually have much (lower/higher) temperature coefficients of resistance than pure metals.
(c) The resistivity of the alloy manganin is nearly independent of/ increases rapidly with increase of temperature.
(d) The resistivity of a typical insulator (e.g., amber) is greater than that of a metal by a factor of the order of (1022/1023).

Solution: (a) greater (b) lower (c) nearly independent of (d) 1022

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Answer the following questions:
(a) A steady current flows in a metallic conductor of the non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?
(b) Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements that do not obey Ohm’s law.
(c) A low voltage supply from which one needs high currents must have very low internal resistance. Why?
(d) A high tension (HT) supply of, say, 6 kV must have a very large internal resistance. Why?

Answer: (a) The current is assumed to be constant. As a result, it's a constant. The area of cross-section has an inverse relationship with current density, electric field, and drift speed. (b) No,...

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Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables. (ρAl = 2.63 × 10–8 Ω m, ρCu = 1.72 × 10–8 Ω m, Relative density of Al = 2.7, of Cu = 8.9.)

Answer – According to the question statement, some given properties of aliminium are – Length = l1 Resistance = R Resistivity ,ρAI =ρ1= 2.63×10−8 Ωm Relative density , d1 = 2.7 Area...

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(a) Six lead-acid type of secondary cells each of emf 2.0 V and internal resistance 0.015 Ω are joined in series to provide a supply to a resistance of 8.5 Ω. What is the current drawn from the supply and its terminal voltage?
(b) A secondary cell after long use has an emf of 1.9 V and a large internal resistance of 380 Ω. What maximum current can be drawn from the cell? Could the cell drive the starting motor of a car?

Answer – According to the question statement, (a) Emf of the secondary cells is ε = 2.0 V N is the number of secondary cells  = 6 Then total EMF is given by – E = nε = 6 x 2 E = 12 V r  =...

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The earth’s surface has a negative surface charge density of 10–9 C m–2. The potential difference of 400 kV between the top of the atmosphere and the surface results (due to the low conductivity of the lower atmosphere) in a current of only 1800 A over the entire
globe. If there were no mechanism of sustaining atmospheric electric field, how much time (roughly) would be required to neutralise the earth’s surface? (This never happens in practice because there is a mechanism to replenish electric charges, namely the continual thunderstorms and lightning in different parts of the globe). (Radius of earth = 6.37 × 10m.)

Answer – According to the question statement, Surface charge density of the earth is σ = 10−9 cm−2Potential difference between the surface and the top of the atmosphere is V= 400 kVCurrent over...

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The number density of free electrons in a copper conductor estimated in Example 3.1 is 8.5 × 1028 m–3. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 × 10–6 m2 and it is carrying a current of 3.0 A.

Answer – It is given that Number density of free electrons in a copper conductor is n =  8.5 x 10 28 m – 3 Assume that the Length of the copper wire is denoted by l and we have l...

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A storage battery of emf 8.0 V and internal resistance 0.5 Ω is being charged by a 120 V dc supply using a series resistor of 15.5 Ω. What is the terminal voltage of the battery during charging? What is the
purpose of having a series resistor in the charging circuit?

Answer – According to the question statement – The EMF of storage battery is E = 8.0 V Internal resistance of battery is given by r = 0.5 Ω DC supply voltage is V = 120 V Resistance of the resistor...

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A ) In a meter bridge given below, the balance point is found to be at 39.5 cm from the end A, when the resistor S is of 12.5 Ω. Determine the resistance of R. Why are the connections between resistors in a Wheatstone or meter bridge made of thick copper strips?

B ) Determine the balance point of the bridge above if R and S are interchanged. C ) What happens if the galvanometer and cell are interchanged at the balance point of the bridge? Would the...

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A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds to a steady value of 2.8 A. What is the steady temperature of the heating
element if the room temperature is 27.0 °C? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 × 10
–4 °C–1.

Answer – According to the question; Supply voltage,  V = 230 V initial current drawn is given by I 1 = 3.2 A Let the initial resistance be given by R 1, which can be determined...

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At room temperature (27.0 °C) the resistance of a heating element is 100 Ω. What is the temperature of the element if the resistance is found to be 117 Ω, given that the temperature coefficient of the material of the resistor is 1.70 × 10–4 °C–1.

Answer – We are given that,  Room temperature, T = 27 ° C Resistance of heating element , R = 100 Ω Let the increased temperature of the filament be given by T 1 At T 1, the...

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Monochromatic light of wavelength 632.8 \mathrm{~nm} is produced by a helium-neon laser. The power emitted is 9.42 \mathrm{~mW} (a) Find the energy and momentum of each photon in the light beam
(b) How many photons per second, on the average, arrive at a target irradiated by this beam? (Assume the beam to have a uniform cross-section which is less than the target area)

Wavelength of a monochromatic light is given as $\lambda=632.8 \mathrm{~nm}=632.8 \times 10^{-9} \mathrm{~m}$ Power emitted by the laser is, $P=9.42 \mathrm{~mW}=9.42 \times 10^{-3} \mathrm{~W}$...

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A monoenergetic (18 keV) electron beam initially in the horizontal direction is subjected to a horizontal magnetic field of 0.04 G normal
to the initial direction. Estimate the up or down deflection of the beam over a distance of 30 cm (me
= 9.11 × 10–31 kg). [Note: Data in this exercise are so chosen that the answer will give you an idea of
the effect of earth’s magnetic field on the motion of the electron beam from the electron gun to the screen in a TV set.]

Answer – Energy of the electron beam is given by E = 18 keV Or, E = 18 x 103 eV = 18 x 103 x 1.6 x 10-19 J Magnetic field is given by B = 0.04 G Mass of the electron is given by...

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A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60°, and one of the fields has a magnitude of 1.2 × 10–2 T. If the dipole comes to stable equilibrium at an angle of 15° with this field, what is the magnitude of the other field?

Answer- Magnitude of one of the magnetic field is given by B1 = 1.2 × 10–2 T Suppose that the magnitude of the other field is B2 And the angle between the field is given, θ = 60° We...

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A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12 cm. The coil is in a vertical plane making an angle of 45° with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west to east.
(a) Determine the horizontal component of the earth’s magnetic field at the location.
(b) The current in the coil is reversed, and the coil is rotated about its vertical axis by an angle of 90° in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the places to be zero.

Answer: Number of turns is given = 30 Radius of the coil is given = 12 cm Current in the coil is given = 0.35 A Angle of dip, given by δ = 450 (a) Horizontal component of earth’s magnetic field...

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A telephone cable at a place has four long straight horizontal wires carrying a current of 1.0 A in the same direction east to west. The earth’s magnetic field at the place is 0.39 G, and the angle of dip is 35°. The magnetic declination is nearly zero. What are the resultant magnetic fields at points 4.0 cm below the cable?

Answer – First it is important to decide the direction which would best represent the given situation. We are given that BH = B cos δ = 0.39 × cos 35o G Therefore, BH =...

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A long straight horizontal cable carries a current of 2.5 A in the direction 10° south of west to 10° north of east. The magnetic meridian
of the place happens to be 10° west of the geographic meridian. The earth’s magnetic field at the location is 0.33 G, and the angle of dip is zero. Locate the line of neutral points (ignore the thickness of the
cable)? (At neutral points, magnetic field due to a current-carrying the cable is equal and opposite to the horizontal component of earth’s magnetic field.)

Answer – Current in the wire is given by 2.5 A The earth’s magnetic field at a location is given by R= 0.33 G = 0.33 x 10-4 T Angle of dip is zero is given by δ = 0 Horizontal...

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Answer the following questions:
(a) Explain qualitatively on the basis of domain picture the irreversibility in the magnetisation curve of a ferromagnet.
(b) The hysteresis loop of a soft iron piece has a much smaller area than that of a carbon steel piece. If the material is to go through repeated cycles of magnetisation, which piece will dissipate greater heat energy?
(c) ‘A system displaying a hysteresis loop such as a ferromagnet, is a device for storing memory?’ Explain the meaning of this statement.
(d) What kind of ferromagnetic material is used for coating magnetic tapes in a cassette player, or for building ‘memory stores’ in a modern computer?
(e) A certain region of space is to be shielded from magnetic fields. Suggest a method.

Answer – (a) When a substance is placed in an external magnetic field, the domain aligns in the direction of the magnetic field. The process of alignment consumes some energy. The substance retains...

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Answer the following questions:
(a) Why does a paramagnetic sample display greater magnetisation (for the same magnetising field) when cooled?
(b) Why is diamagnetism, in contrast, almost independent of temperature?
(c) If a toroid uses bismuth for its core, will the field in the core be (slightly) greater or (slightly) less than when the core is empty?
(d) Is the permeability of a ferromagnetic material independent of the magnetic field? If not, is it more for lower or higher fields?
(e) Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at
every point.) Why?
(f) Would the maximum possible magnetisation of a paramagnetic sample be of the same order of magnitude as the magnetisation
of a ferromagnet?

Answer – (a) At a lower temperature, thermal motion is reduced, and the tendency to disturb the alignment of the dipoles is reduced. (b) The induced dipole moment is always in the opposite direction...

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A short bar magnet of magnetic moment 5.25 × 10–2 J T–1 is placed with its axis perpendicular to the earth’s field direction. At what distance from the centre of the magnet, the resultant field is inclined at 45° with earth’s field on (a) its normal bisector and (b) its axis. The magnitude of the earth’s field at the place is given to be 0.42 G. Ignore the length of the magnet in comparison to the distances involved.

Answer : Magnetic moment of the bar magnet is given by M = 5.25 × 10–2 J T–1  Magnitude of earth’s magnetic field at a place is given by H = 0.42 G = 0.42×10-4 T The magnetic field on the...

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A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the axis of the magnet at 14 cm from the centre of the magnet. The
earth’s magnetic field at the place is 0.36 G and the angle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the null–point (i.e., 14 cm) from the centre of the magnet? (At null points, field due to a magnet is equal and opposite to the horizontal component of earth’s magnetic field.)

Answer : Earth’s magnetic field at the given place is given by H = 0.36 G The magnetic field at distance d from the axis of the magnet can be calculated using the following formula –...

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A short bar magnet has a magnetic moment of 0.48 J T–1. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on (a) the axis,
(b) the equatorial lines (normal bisector) of the magnet.

Magnetic moment of the bar magnet is given by M = 0.48 J T–1 Distance, d = 10 cm = 0.1 m The magnetic field at distance d from the magnet's centre on the axis can be calculated using the following...

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At a certain location in Africa, a compass points 12° west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points 60° above the
horizontal. The horizontal component of the earth’s field is measured to be 0.16 G. Specify the direction and magnitude of the earth’s field at the location.

Answer – We are given the angle of declination, θ = 12° Angle of dip, given by δ = 60° Horizontal component of earth’s magnetic field is given by BH = 0.16 G Earth’s magnetic field at the given...

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A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at 22° with the horizontal. The horizontal component of the earth’s magnetic field
at the place is known to be 0.35 G. Determine the magnitude of the earth’s magnetic field at the place.

Answer – Horizontal component of earth’s magnetic field is given by BH = 0.35 G Angle made by the needle with the horizontal plane is known as the Angle of dip, given by δ=22° Earth’s magnetic field...

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A circular coil of 16 turns and radius 10 cm carrying a current of 0.75 A rests with its plane normal to an external field of magnitude 5.0 × 10–2 T. The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of 2.0 s–1. What is the moment of inertia of the coil about its axis of rotation?

Answer – Number of turns in the circular coil is given by N = 16 Radius of the coil is given by r = 10 cm = 0.1 m Cross-section of the coil, A is given by – $A=\pi {{r}^{2}}=\pi {{(0.1)}^{2}}$...

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A line charge λ per unit length is lodged uniformly onto the rim of a wheel of mass M and radius R. The wheel has light non-conducting spokes and is free to rotate without friction about its axis. A uniform magnetic field extends over a circular region within the rim. It is given by,

\[B=-{{B}_{0}}k(r\le a;a<R)\] = 0 (otherwise) What is the angular velocity of the wheel after the field is suddenly switched off? Answer – Line charge per unit length is given by the expression –...

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We have an air-cored solenoid having a length of 30 cm, whose area is 25cm2 and a number of turns are 500. And the solenoid has carried a current of 2.5 A. Suddenly the current is turned off and the time is taken for it is 10−3s. What would be the average value of the induced back -emf by the ends of the open switch in the circuit? (Neglect the variation in the magnetic fields near the ends of the solenoid.)

Answer – Given, Length of the solenoid is given by l = 30 cm = 0.3 m Area of the solenoid, then becomes  A =25 cm2 = 25 × 10−4m2 Number of turns on the solenoid is given by N = 500 Current in...

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In the given figure we have a metal rod PQ which is put on the smooth rails AB and these are kept in between the two poles of permanent magnets. All these three (rod, rails and the magnetic field ) are in mutually perpendicular direction. There is a galvanometer ‘G’ connected through the rails by using a switch ‘K’. Given, Rod’s length = 15 cm , Magnetic field strength, B = 0.50 T, Resistance produced by the closed-loop = 9.0mΩ. Let’s consider the field is uniform.

(i) Determine the polarity and the magnitude of the induced emf if we will keep the K open and the rod will be moved with the speed of 12 cm/s in the direction shown in the figure.  (ii) When...

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We have a powerful loudspeaker magnet and have to measure the magnitude of the field between the poles of the speaker. And a small search coil is placed normal to the field direction and then quickly removed out of the field region, the coil is of 2cm2 area and has 25 closely wound turns. Similarly, we can give the coil a quick 90 degree turn to bring its plane parallel to the field direction. We have measured the total charge flown in the coil by using a ballistic galvanometer and it comes to 7.5 mC. Total resistance after combining the coil and the galvanometer is 0.50Ω. Estimate the field strength of the magnet.

Ans: Given, Coil’s Area is A = 2cm2 = 2×10-4m2 Number of turns on the coil is given by N = 25 Total Charge in the coil is given by Q = 7.5 mC = 7.5×10−3C The combo of coil and galvanometer...

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We have a square loop having side as 12 cm and its sides are parallel to x and y-axis is moved with a velocity of 8 cm /s in the positive x-direction in a region which have a magnetic field in the direction of positive z-axis. The field is not uniform whether in case of its space or in the case of time. It has a gradient of 10−3 T cm−1 along the negative x-direction(i.e its value increases by 10−3 T cm−1 as we move from positive to negative direction ), and it is reducing in the case of time with the rate of 10−3 T s−1 . Calculate the magnitude and direction of induced current in the loop (Given: Resistance = 4.50mΩ).

Answer – We have, Side of the Square loop is given by s = 12cm = 0.12m Area of the loop becomes –  A = s × s = 0.12 × 0.12 A = 0.0144 m2 Velocity of the loop is given by v = 8 cm-1 =...

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Let us assume that the loop in question number 4 is stationary or constant but the current source which is feeding the electromagnet which is producing the magnetic field is slowly decreased. It was having an initial value of 0.3 T and the rate of reducing the field is 0.02 T / sec. If the cut is joined to form the loop having a resistance of 1.6 \Omega1.6Ω. Calculate how much power is lost in the form of heat? What is the source of this power?

Answer – A rectangular loop is given having sides as 8 cm and 2 cm. Therefore, the area of the loop will be will be given by  A = L × B A = 8 cm × 2 cm = 16 cm2 A = 16×10−4m2 Value of...

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A jet plane is travelling towards the west at a speed of 1800 km/h. What is the voltage difference developed between the ends of the wing having a span of 25 m, if the Earth’s magnetic field at the location
has a magnitude of 5 × 10
–4 T and the dip angle is 30°.

Answer – We have been provided the following data – Speed of the plane with which it is moving is given by  v = 1800 km/h = 500 m/s Wing span of the jet is given by l = 25 m Magnetic field...

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Question 12.19: An organic compound contains 69.77% carbon, 11.63% hydrogen and rest oxygen. The molecular mass of the compound is 86. It does not reduce Tollens’ reagent but forms an addition compound with sodium hydrogensulphite and give positive iodoform test. On vigorous oxidation it gives ethanoic and propanoic acid. Write the possible structure of the compound.

Solution: The number of carbon, hydrogen, and oxygen atoms in an organic compound can thus be expressed as: Therefore, the empirical formula of the compound is C5H10O. Now, the empirical formula...

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Question 12.18: Give a plausible explanation for: (iii) During the preparation of esters from a carboxylic acid and an alcohol in the presence of an acid catalyst, the water or the ester should be removed as soon as it is formed.

Solution: In the presence of an acid, an ester along with water is generated reversibly from a carboxylic acid and an alcohol. Because the reaction is reversible, if either water or ester is not...

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A short bar magnet of magnetic moment m = 0.32 JT–1 is placed in a uniform magnetic field of 0.15 T. If the bar is free to rotate in the plane of the field, which orientation would correspond to its (a) stable, and (b) unstable equilibrium? What is the potential energy of the magnet in each case?

Answer – Moment of the bar magnet is given by M = 0.32 JT–1  External magnetic field, is given by B = 0.15 T The magnetic field is aligned with the bar magnet. This system is said to be in...

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A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s–1 in a uniform horizontal magnetic field of magnitude 3.0 × 10–2 T. Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance 10 Ω, calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?

Answer –        Maximum emf induced is given = 0.603 V Average emf induced is given by= 0 V Maximum current in the coil = 0.0603 A Power loss (average) is given =...

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A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of the uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm s–1 in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?

Answer – Length of the wired loop is given by l = 8 cm = 0.08 m Width of the wired loop is given by b = 2 cm = 0.02 m Since the loop is a rectangle, the area of the wired loop is given by – A = lb =...

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A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?

Answer – We are given - Number of turns – 15 turns / cm = 1500 turns / m Number of turns per unit length is given by n = 1500 turns The solenoid has a small loop of area which is given by A = 2.0...

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We are rotating a 1 m long metallic rod with an angular frequency of 400 red s^{-1}s−1 with an axis normal to the rod passing through its one end. And on to the other end of the rod, it is connected with a circular metallic ring. There exist a uniform magnetic field of 0.5 T which is parallel to the axis everywhere. Find out the emf induced between the centre and the ring.

Answer – Length of the rod is given = 1m Angular frequency is given by = ω = 400 rad/sec Magnetic field strength is given by B = 0.5 T The rod has zero linear velocity at one end and a linear...

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