The radius of a loop as shown in the figure is \(10~\mathrm {cm}.\) If the magnetic field is uniform and has a value \(10^{-2}~ T,\) then the flux through the loop will be:
 

1.	\(2 \pi \times 10^{-2}Wb\)	2.	\(3 \pi \times 10^{-4}Wb\)
3.	\(5 \pi \times 10^{-5}Wb\)	4.	\(5 \pi \times 10^{-4}Wb\)

The dimensions of inductance are:

$1.$ $\left[ML{T}^{-2}{A}^{-2}\right]$
$2.$ $\left[M{L}^2{T}^{-2}{A}^2\right]$
$3.$ $\left[M{L}^2{T}^{-2}{A}^{-1}\right]$
$4.$ $\left[M{L}^2{T}^{-2}{A}^{-2}\right]$

If a current is passed through a circular loop of radius R then magnetic flux through a coplanar square loop of side l as shown in the figure (l<<R) is:

1. $\frac{{\mu }_{0}l}{2}\frac{R^2}{l}$

2. $\frac{{\mu }_{0}I{l}^2}{2R}$

3. $\frac{{\mu }_{0}l{\mathrm{\pi R}}^2}{2l}$

4. $\frac{{\mu }_0{\mathrm{\pi R}}^{2}I}{l}$

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. $\frac{4{\mu }_0}{\mathrm{\pi }}$

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. \(t=5~\text{s}\)

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

Eddy currents are used in:

1. Induction furnace

2. Electromagnetic brakes

3. Speedometers

4. All of these

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:

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

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