A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A constant magnetic field B exists as shown in the figure. Mechanical power required to maintain its uniform velocity is

1. $\frac{B^2{L}^2{v}^2}{R}$

2. $\frac{B^2{L}^2{v}^2}{2R}$

3. $\frac{B^2{L}^2{v}^2}{4R}$

4. Zero

A conducting disc of radius r rotates about its axis with an angular speed $\omega$ in a uniform magnetic field B perpendicular to the plane of the disc as shown. A resistance R is connected between centre and rim of the disc, then-

1. No e.m.f. will induce across the resistance

2. E.m.f. will induce and A is at high potential

3. Current in resistance will flow from A to B

4. Resistance becomes hot due to Joule's heating

A train is moving on a straight horizontal track. Induced emf across the axle is maximum when it moves

1. At poles

2. At equator

3. Along the direction where the angle of dip is 45$°$

4. Emf is not induced

A square loop enters a magnetic field with velocity v as shown in the figure. The front edge enters the magnetic field at time t = 0. Which of the following graphs gives the correct variation of emf$\epsilon$ induced in the loop with time t for its constant velocity in the magnetic field? [Take anticlockwise current as negative and vice versa]

A rectangular metal loop ABCD of is passed through the magnetic field with a constant velocity v. Which of the following represents power (P) dissipated vs time (t) graph?

1.                2. 
3.                4. 

Self-inductance of a solenoid is 5 mH. If the current is decreasing through it at the rate 10⁺³ A/s, then emf induced in the solenoid is

1. -5V

2. 5V

3. 2.5V

4. -2.5V

Keeping number of turns constant self inductance L of a solenoid varies with its length l as

1. L$\propto$l

2. L$\propto \frac{1}{\mathrm{l}}$

3. L$\propto {\mathrm{l}}^2$

4. L$\propto \frac{1}{{\mathrm{l}}^2}$

A conducting rod AC of length 4l is rotated with angular velocity $\omega$ about a point O in a uniform magnetic field $\overrightarrow{B}$ directed into the plane of the paper. If AO = l and OC = 3l, then the potential difference between A and C, V_A - V_C is

1. $2{\mathrm{B\omega l}}^2$

2. ${\mathrm{B\omega l}}^2$

3. $3{\mathrm{B\omega l}}^2$

4. $4{\mathrm{B\omega l}}^2$

A flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of the circle. The radius \(r\) of the circle changes with time \(t\) as shown in the figure. The graph of the magnitude of induced emf \(|\varepsilon|\) versus time \(t\) in the circle is represented by:

1.		2.
3.		4.

A cylindrical space of radius \(R\) is filled with a uniform magnetic induction \(B\) parallel to the axis of the cylinder. If \(B\) changes at a constant rate, the graph showing the variation of the induced electric field with distance \(r\) from the axis of the cylinder is:

1.		2.
3.		4.