A circular loop of radius R carrying current i lies in the x-y plane. If the centre of the loop coincides with the origin, then the total magnetic flux passing through the x-y plane will be:

1.	directly proportional to I.
2.	directly proportional to R.
3.	directly proportional to R2.
4.	Zero.

A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region:

1. is zero
2. decreases as $\frac{1}{r}$
3. increases as r
4. decreases as $\frac{1}{r^2}$

Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be:

A conducting rod of length 2l is rotating with constant angular speed $\omega$ about its perpendicular bisector. A uniform magnetic field $\overrightarrow{B}$ exists parallel to the axis of rotation. The e.m.f. induced between the two ends of the rod is:

1. \(B\omega l^2\)
2. $\frac{1}{2}B\omega l^2$
3. $\frac{1}{8}B\omega l^2$
4. Zero

A conductor ABOCD moves along its bisector with a velocity of 1 m/s through a perpendicular magnetic field of \(1~\mathrm{wb/m^2}\), as shown in fig. If all the four sides are of 1 m length each, then the induced emf between points A and D is:
        
1. 0

2. 1.41 volt

3. 0.71 volt

4. None of the above

A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical rails are connected to each other with a resistance R between a and b. A uniform magnetic field B is applied perpendicular to the plane abcd such that cd moves with a constant velocity of:

A conducting rod AC of length 4l is rotated about point O in a uniform magnetic field $\overrightarrow{B}$ directed into the paper. If AO = l and OC = 3l, then:

1. $V_A-V_O=\frac{B\omega l^2}{2}$
2. $V_O-V_C=\frac{7}{2}B\omega l^2$
3. $V_A-V_C=4B\omega l^2$
4. $V_C-V_O=\frac{9}{2}B\omega l^2$

The graph gives the magnitude \(B(t)\) of a uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop, greatest first:

A square loop of side 5 cm enters a magnetic field with 1 cms^-1. If the front edge enters the magnetic field at t = 0, then which graph best depicts emf?

1.		2.
3.		4.

A coil having number of turns N and cross-sectional area A is rotated in a uniform magnetic field B with an angular velocity $\mathrm{\omega }$. The maximum value of the emf induced in it is:

1. $\frac{\mathrm{NBA}}{\mathrm{\omega }}$                             

2. $\mathrm{NBA\omega }$

3. $\frac{\mathrm{NBA}}{{\mathrm{\omega }}^2}$                             

4. ${\mathrm{NBA\omega }}^2$