Two coils of self-inductance L₁ and L₂ are placed so close together that they completely link the magnetic flux of each other. If M be their mutual inductance then, the correct relation is 

1. M = $\sqrt{\frac{L_1}{L_2}}$

2. M = L₁$\sqrt{L_2}$

3. M = L₁L₂

4. M = $\sqrt{L_1{L}_2}$

Calculate the self-inductance of a solenoid having \(1000\) turns and length \(1\) m. (The area of cross-section is \(7\) cm² and \(\mu_r=1000).\)

1. \(888\) H

2. \(0.88\) H

3. \(0.088\) H

4. \(88.8\) H

Two discs of radii R and 2R are moving with velocities v and 2v in opposite directions on a conducting platform, as shown in the figure. If magnetic field B is applied in the plane perpendicular to the discs, then the potential difference between two points P and Q which are the topmost points of the discs is 

1. 8BRv

2. 4BRv

3. 10BRv

4. 2BRv

What is the effective self-inductance of two solenoids in series-wound on a core as shown in the figure, if L is the self-inductance of each solenoid?

1. L

2. 2L

3. L/2

4. Zero

A uniform conductor having length l is moving in uniform magnetic field B with speed v. If B, l and v are mutually perpendicular and R is the resistance of the conductor, then the power delivered by the external source is

1. B²l²v²/2R

2. 2B²l²v²/R

3. B²l²v²/R

4. Zero

A circular ring of radius \(r\) is at the centre of a square having side  \(a\left ( a\gg r \right ).\) The mutual inductance of the system is:
1. \( \frac{\mu_0 r^2}{a}\)
2. \( \frac{\sqrt{2} \mu_0 r^2}{\pi} \)
3. \(\frac{2 \sqrt{2} \mu_0 r^2}{a}\)
4. \( \frac{2 \sqrt{2} \mu_0 r^2}{\pi a}\)

If a semicircular conducting loop \(ACB\) is rotating in the plane of paper with constant angular velocity \(\omega\) about \(O\), then which of the following graphs shows the variation of induced current \((I)\) with time \((t)\)? The magnetic field is perpendicular to the plane of the loop as shown in the figure.
               

1.		2.
3.		4.

A current-carrying cable is penetrating a loop as shown in the figure. If the magnitude of the current is decreasing with time, then the current induced in the loop is

1. Zero

2. Clockwise

3. Anticlockwise

4. Depends on the magnitude of the current

A solenoid has an inductance of 20 H and a resistance of 5 ohms. It is connected to a battery of 20 volts. The maximum magnetic energy stored in the magnetic field of the solenoid is

1. 40 J

2. 160 J

3. 320 J

4. 80 J

The slotting processes in a metallic sheet results in: