A rod having length \(l\) and resistance \(R_0\) is moving with a speed \(v\) as shown in the figure. The current through the rod is:
                            

1. \(\dfrac{B l v}{\frac{R_{1} R_{2}}{R_{1} + R_{2}} + R_{0}}\)

2. \(\dfrac{Blv}{\left(\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{o}}\right)^{2}}\)

3. \(\dfrac{B l v}{R_{1} + R_{2} + R_{0}}\)

4. \(\dfrac{B l v}{\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{0}}}\)

The coefficient of mutual inductance between two coils depends upon:

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. \(\dfrac{\mu_{0} \pi R^{2} I}{l}\)