Dependence on Magnetic Field

Q. The deflection in a moving coil galvanometer falls from $50$ divisions to $10$ divisions when a shunt of $12\Omega$ is connected with it. The resistance of galvanometer coil is ?

1. $12\Omega$
2. $36\Omega$
3. $48\Omega$
4. $24\Omega$

Q. Find the $ϵ$ mf induced in the square frame.

1. $\frac{{\mu }_{0}a}{2\pi }ln\left(\frac{b+a}{b}\right)(2t+3)$
2. $\frac{{\mu }_{0}a}{2\pi }ln\left(\frac{b+a}{b}\right)(t^2+3t)$
3. $Zero$
4. $\frac{{\mu }_{0}a}{\pi }ln\left(\frac{b+a}{b}\right)(2t+3)$

Q. An infinitely long cylinder is kept parallel to a uniform magnetic field B directed along positive z axis. The direction of induced current as seen from the z axis will be

1. Clockwise of the +ve z axis
2. Anticlockwise of the +ve z axis
3. Zero
4. Along the magnetic field

Q. Find $i_{ind}$ for the ring of radius R if $B=\propto t^2$. The resistance/length is $\lambda$.

1. $\frac{2\propto Rt}{\lambda }$
2. $\frac{\propto Rt}{\lambda }$
3. $\frac{\propto R{t}^2}{\lambda }$
4. $\frac{2\propto R{t}^2}{\lambda }$

Q.

A hundred turns of insulated copper wire are wrapped around an iron cylinder of area ${10}^{-3}{m}^2$ and are connected to a resistor. The total resistance in the circuit is 10 ohms. If the longitudinal magnetic induction in the iron changes from 1 weber $m^{-2}$, in one direction to 1 Weber $m^{-2}$ in the opposite direction, how much charge flows through the circuit?

1. $2\times {10}^{-2}$C

2. $2\times {10}^{-3}$C

3. $2\times {10}^{-4}$C

4. $2\times {10}^{-5}$C