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.	\(\dfrac{L}{l}\)	2.	\(\dfrac{l}{L}\)
3.	\(\dfrac{L^2}{l}\)	4.	\(\dfrac{l^2}{L}\)

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. \(5\pi~\text{V}\)
2. \(2\pi~\text{V}\)
3. \(4\pi~\text{V}\)
4. \(\pi~\text{V}\)

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:

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:

          
1. \(\dfrac{\mu_{0} I}{2} \dfrac{R^{2}}{l}\)
2. \(\dfrac{\mu_{0} I l^{2}}{2 R}\)
3. \(\dfrac{\mu_{0}I \pi R^{2}}{2 l}\)
4. \(\dfrac{\mu_{0} \pi R^{2} I}{l}\)

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

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R):