A long solenoid of diameter 0.1m has 2$\times {10}^4$ turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01m is placed with its axis coinciding with the solenoid's axis.  The current in the solenoid reduces at a constant rate to 0 A 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. 32$\mathrm{\pi \mu C}$

2. 16$\mu C$

3. 32$\mu C$

4. 16$\mathrm{\pi \mu C}$

A thin semicircular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B,as shown in figure. The potential difference developed across the ring when its speed is v,is


(1) zero

(2) Bvπr²/2 and P is at higher potential

(3) πrBv and R is at higher potential  

(4) 2rBv and R is at higher potential

A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced emf is

(1) once per revolution

(2) twice per revolution

(3) four times per revolution

(4) six times per revolution

A coil of resistance 400$\Omega$ is placed in a magnetic field. If the magnetic flux $\varphi \left(Wb\right)$ linked with the coil varies with time t (sec) as $\varphi =50t^2+4.$

The current in the coil at t=2s is 

(1) 0.5A                                           

(2) 0.1A

(3) 2A                                               

(4) 1A

In a coil of resistance 10$\mathrm{\Omega }$, the induced

current developed by changing magnetic

flux through it is shown in the figure as a 

function of time. The magnitude of change

in flux through the coil in weber is-

(1) 8

(2) 2

(3)6

(4)4

a long solenoid has 500 turns. When a current of 2 A is passed through it, the resulting magnetic flux linked with each turn of the solenoid is $4\times {10}^{-3}$ Wh.  The self-inductance of the solenoid is 

(a) 2.5 h

(b) 2.0 H 

(c) 1.0 H

(d) 4.0 H

The magnetic potential energy stored in a certain inductor is \(25\) mJ, when the current in the inductor is \(60\) mA. This inductor is of inductance:
1. \(0.138\) H
2. \(138.88\) H
3. \(1.389\) H
4. \(13.89\) H

A uniform magnetic field is restricted within a region of radius \(r\). The magnetic field changes with time at a  rate \(\frac{dB}{dt}\). Loop \(1\) of radius \(R>r\) is enclosed within the region \(r\) and loop \(2\) of radius \(R\) is outside the region of the magnetic field as shown in the figure. Then, the emf generated is:
           

An electron moves on a straight-line path \(XY\) as shown. The \(\mathrm{abcd}\) is a coil adjacent to the path of electrons. What will be the direction of current if any, induced in the coil?