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

A rod having length l and resistance R₀ is moving with speed v as shown in the figure. The current through the rod is:
               
1. $\frac{Blv}{{\displaystyle \frac{R_1{R}_2}{R_1+R_2}}+R_0}$

2. $\frac{\mathrm{Blv}}{{\left({\displaystyle \frac{1}{{\mathrm{R}}_1}}+{\displaystyle \frac{1}{{\mathrm{R}}_2}}+{\displaystyle \frac{1}{{\mathrm{R}}_{\mathrm{o}}}}\right)}^2}$

3. $\frac{Blv}{R_1+R_2+R_0}$

4. $\frac{Blv}{{\displaystyle \frac{1}{R_1}}+{\displaystyle \frac{1}{R_2}}+{\displaystyle \frac{1}{R_0}}}$

A solenoid of inductance L and resistance R is connected to a battery of e.m.f. E. Maximum value of magnetic energy stored in the inductor is:

$1.$ $\frac{E^2}{2R}$
$2.$ $\frac{E^{2}L}{2R^2}$
$3.$ $\frac{E^{2}L}{R}$ $$
$4.$ $\frac{E^{2}L}{2R}$

The coefficient of mutual inductance between two coils depends upon:

A small square loop of wire of side 'l' is placed inside a large square loop of side 'L' (L$\gg$l). If the loops are coplanar and their centres coincide, the mutual inductance of the system is directly proportional to:

1. L/l

2. l/L

3. L²/l

4. l²/L

Two coils have a mutual inductance of 5 mH. The current changes in the first coil according to the equation \(I=I_{0}cos\omega t,\) where \(I_{0}=10~A\) and $\omega$ = 100$\pi$ rad/s. The maximum value of e.m.f. induced in the second coil is:

1. 5$\pi$ Volt

2. 2$\pi$ Volt

3. 4$\pi$ Volt

4. $\pi$ Volt

The current through a choke coil increases from zero to 6 A in 0.3 seconds and an induced emf of 30 V is produced. The inductance of the coil is:

A short magnet is allowed to fall along the axis of a horizontal metallic ring. Starting from rest, the distance fallen by the magnet in one second may be:

1. 4 m

2. 5 m

3. 6 m

4. 7 m

The magnetic flux linked with a coil varies with time as \(\phi = 2t^2-6t+5,\) where \(\phi \) is in Weber and \(t\) is in seconds. The induced current is zero at:
1. \(t=0\)
2. \(t= 1.5~\text{s}\)
3. \(t=3~\text{s}\)
4. \(t=5~\text{s}\)

The net magnetic flux through any closed surface, kept in uniform magnetic field is:

1. Zero

2. $\frac{{\mu }_0}{4\mathrm{\pi }}$

3. $4{\mathrm{\pi \mu }}_0$

4. $\frac{4{\mu }_0}{\mathrm{\pi }}$