A small square loop of wire of side \(l\) is placed inside a large square loop of side \(L\) \((L>>l)\). If the loops are coplanar and their centres coincide, the mutual inductance of the system is directly proportional to:
1. \(\frac{L}{l}\)
2. \(\frac{l}{L}\)
3. \(\frac{L^2}{l}\)
4. \(\frac{l^2}{L}\)

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 \(I_{0}=10~\text{A}\)and\(\omega = 100\pi ~\text{rad/s}\). The maximum value of emf induced in the second coil is:
1. \(5\pi\) Volt
2. \(2\pi\) Volt
3. \(4\pi\) Volt
4. \(\pi\) Volt

Eddy currents are used in:

1. Induction furnace

2. Electromagnetic brakes

3. Speedometers

4. All of these

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:

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:

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:

The dimensions of inductance are:

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

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