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Q. No.
A circular wire of radius \(R\) is placed in a uniform magnetic field \(B,\) which acts into the plane as shown. The wire is given a half-turn about a diameter. The resistance per unit length of the wire is \(\lambda.\) The total charge flowing through the wire is:
                              

 
1. \(\dfrac{2BR}{\lambda}\) 2. \(\dfrac{BR}{\lambda}\)
3. \(\dfrac{BR}{2\lambda}\) 4. zero
Subtopic:  Motional emf |
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A triangular wire frame, in the form of an equilateral triangle \(PQR\) moves with a uniform velocity into a region where there is a uniform magnetic field \(B\). The edge \(PQ\) is parallel to the boundary of the region and the velocity \(v\) is perpendicular to it. The emf(\(E\)) induced within the frame is plotted as a function of time \(t,\) starting from when the frame enters the magnetic field. \(E\) is given by:
1. \(Bv^2t\) 2. \(2Bv^2t\)
3. \(\dfrac{\sqrt3}{2}Bv^2t\) 4. \(\dfrac{2}{\sqrt3}Bv^2t\)
Subtopic:  Motional emf |
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A rod \(PQ\) of length \(L\) moves in a uniform magnetic field \(B\) with a velocity \(v,\) perpendicular to its own length. The magnetic field \(B\) acts in the plane of motion, making an angle \(\theta\) with the rod. The motional emf, \(V_P-V_Q\) is:
                 
1. zero
2. \(BLv\cos\theta\)
3. \(BLv\sin\theta\)
4. \(BLv\)
Subtopic:  Motional emf |
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A horizontal conducting metallic wire \(\mathrm{(AB)}\) of length \(L\) falls vertically under gravity. A horizontal magnetic field \((B_H)\) exists in the region, as shown. The emf induced in the wire:
                   
1. is zero 2. is constant
3. increases with time 4. decreases with time
Subtopic:  Motional emf |
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A wire, bent into the shape of a right angled triangle \(PQR,\) lies with its side \(PR\) parallel to a current carrying wire, and side \(QR\) perpendicular to it. The loop lies in the plane of the wire. EMF induced in the loop when it is moved with constant speed along \(PR\) is \(\varepsilon_1\) and it is \(\varepsilon_2\) when moved along \(QR\) with the same constant speed. Then,

1. \(\varepsilon_1=0,\varepsilon_2\neq0\)
2. \(\varepsilon_1\neq0,\varepsilon_2=0\)
3. \(\varepsilon_1=0,\varepsilon_2=0\)
4. \(\varepsilon_1\neq0,\varepsilon_2\neq0\)
Subtopic:  Motional emf |
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A metallic rod of length \(3~\text{m}\) rotates with an angular speed of \(4~\text{rad/s}\) in a uniform magnetic field. The field makes an angle of \(30^{\circ}\) with the plane of rotation. The emf induced across the rod is \(72~\text{mV}\). The magnitude of the field is: 
1. \(4 \times 10^{-3}~\text{T}\)
2. \(8 \times 10^{-3}~\text{T}\)
3. \(16 \times 10^{-3}~\text{T}\)
4. \(48 \times 10^{-3}~\text{T}\)
Subtopic:  Motional emf |
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In the system shown in the figure the horizontal rod falls vertically down under its own weight while retaining electrical contact with parallel rails. There is no resistance in the circuit, and there is a uniform horizontal magnetic field into the plane.

The current through the circuit is \(i\). Then:
1. \(i= CBlg\)
2. \(i> CBlg\)  
3. \(i < CBlg\)
4. \(i= 0\)
Subtopic:  Motional emf |
 52%
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A straight wire \(AB\) of length \(L\) rotates about \(A,\) with an angular speed \(\omega.\) A constant magnetic field \(\mathbf B\) acts into the plane, as shown.
Assertion (A): The average induced electric field within the wire has a magnitude of \(\dfrac12B\omega L.\)
Reason (R): The induced electric field is the motional EMF per unit length, and the motional EMF is \(\dfrac12B\omega L^2.\)
 
1. (A) is True but (R) is False.
2. (A) is False but (R) is True.
3. Both (A) and (R) are True and (R) is the correct explanation of (A).
4. Both (A) and (R) are True but (R) is not the correct explanation of (A).
Subtopic:  Motional emf |
 55%
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An \(L\)-shaped rod \((ABC;AB=BC=a)\) moves in its own plane with a velocity \(v\) parallel to \(AB.\) There is a uniform magnetic field \(B\) acting into the plane as shown. The emf developed between \(A,C\) is:
                            
1. \(Bav\)
2. \(\sqrt2Bav\)
3. \(\dfrac{Bav}{2}\)
4. zero
Subtopic:  Motional emf |
 57%
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A horizontal square loop of area \(A\) has \(n\) turns of wire. It is immersed in a uniform, rotating magnetic field \(B\) which is initially perpendicular to the plane of the loop. The field rotates with an angular speed \(\omega\) about a diagonal of the loop. The EMF induced across the loop is:                   
              
1. constant, of magnitude \(n\omega BA\).
2. increasing with time \(t\), of magnitude \(n\omega^2BAt\).
3. decreasing with time \(t\), of magnitude \(\dfrac{nBA}{t}\).
4. sinusoidal with time \(t\), of amplitude \(n\omega BA\).
Subtopic:  Motional emf |
 58%
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