Field Due to a Solenoid

Q. A constant current of $2\text{A}$ is passing through a solenoid of inductance $12\text{H}$. Then,

1. Emf induced across solenoid 8 volt.
2. Emf induced across solenoid 6 volt.
3. Potential difference across solenoid is 0 volt.
4. Potential difference across solenoid is 8 volt.

Q.

A longer solenoid of diameter $0.1m$ has $2\times {10}^4$ turns per meter. At the center of the solenoid, a coil of $100$ turns and radius $0.01m$ is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to $0A$ from $4A$ in $0.05s$. If the resistance of the coil is $10{\pi }^2\Omega$, the total charge flowing through the coil during this time is

1. $26\pi \mu C$
2. $32\mu C$
3. $16\pi \mu C$
4. $32\pi \mu C$

Q. A long solenoid of radius R carries a time $\left(t\right)$ dependent current $I\left(t\right)=I_{0}t(1-t)$. A ring of radius $2R$ is placed coaxially near its middle. During the time instant $0\le t\le 1$, the induced current ($I_R$) and the induced EMF ($V_R$) in the ring changes as:

1. Direction of $I_R$ remains unchanged and $V_R$ is maximum at $t=0.5$
2. Direction of $I_R$ remains unchanged and $V_R$ is zero at $t=0.25$
3. At $t=0.5$ direction of $I_R$ reverses and $V_R$ is zero
4. At $t=0.25$ direction of $I_R$ reverses and $V_R$ is maximum

Q.

An ideal solenoid of cross-sectional area ${10}^{-4}{m}^2$ has 500 turns per metre. At the centre of this solenoid, another coil of 100 turns is wrapped closely around it. If the current in the coil changes from 0 to 2 A in 3.14 millisecond, the emf developed in the second coil is

1. 1 mV

2. 2 mV

3. 3 mV

4. 4 mV

Q. A rod of length $l=0.5\text{m}$ is rotating with an angular speed $\omega =10\text{rad/s}$ about its one end which is at a distance $a=1\text{m}$ from an infinitely long wire carrying current $i=1\text{A}.$ Find the emf induced in the rod at the instant shown in the figure. Rod and wire both are lying in the same plane.

1. $4\times {10}^{-6}[1-\ln (2\left)\right]\text{V}$
2. $0\text{V}$
3. $2\times {10}^{-6}[0.5-\ln (1.5\left)\right]\text{V}$
4. $2\times {10}^{-6}[2-\ln (3\left)\right]\text{V}$

Q.

The mutual inductance between two planar concentric rings of radii $r_{1}and{r}_2(with{r}_1>>r_2)$ placed in air is given by

1. $\frac{{\mu }_0\pi r_2^2}{2r_1}$

2. $\frac{{\mu }_0\pi r_1^2}{2r_2}$

3. $\frac{{\mu }_0\pi (r_1+r_2{)}^2}{2r_1}$

4. $\frac{{\mu }_0\pi (r_1+r_2{)}^2}{2r_2}$