In a circuit with a coil of resistance 2 ohms, the magnetic flux changes from 2.0 Wb to 10.0 Wb in 0.2 second. The charge that flows in the coil during this time is:
1. 5.0 coulomb
2. 4.0 coulomb
3. 1.0 coulomb
4. 0.8 coulomb

A long solenoid of diameter 0.1 m has 2$\times {10}^4$ turns per meter. At the centre of the solenoid, a coil of 100 turns and a radius of 0.01 m is placed with its axis coinciding with the solenoid's axis.  The current in the solenoid reduces at a constant rate from 0 A to 4 A in 0.05 s. If the resistance of the coil is $10{\pi }^{\mathrm{2 }}\Omega$, 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 conducting square frame of side 'a' and a long straight wire carrying current i are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity v. The emf induced in the frame will be proportional to:
      
1. 1/x²
2. 1/(2x-a)²
3. 1/(2x+a)²
4. 1/(2x-a) x (2x+a)

In the figure shown a square loop $\mathrm{PQRS}$ of side $‘\mathrm{a}’$ and resistance $‘\mathrm{r}’$ is placed near an infinitely long wire carrying a constant current $\mathrm{I}$. The sides $\mathrm{PQ}$ and $\mathrm{RS}$ are parallel to the wire. The wire and the loop are in the same plane. The loop is rotated by $180°$ about an axis parallel to the long wire and passing through the midpoints of the side $\mathrm{QR}$ and $\mathrm{PS}$. The total amount of charge which passes through any point of the loop during rotation is:

The number of turns in a coil of wire of fixed radius & length is 600 and its self-inductance is 108 mH. The self-inductance of a coil of 500 turns will be:

1.  74 mH

2.  75 mH

3.  76 mH

4.  77 mH

A magnetic rod is inside a coil of wire which is connected to an ammeter. If the rod is stationary, which of the following statements is true?

A coil of resistance 20 $\Omega$ and inductance 5 H has been connected to a 200 V battery. The maximum energy stored in the coil is:

A magnet is brought towards a coil first (i) speedily (ii) slowly. It can be concluded that the induced e.m.f. and the induced charge in the two cases, will be respectively:

As shown in the figure, a magnet is moved at a fast speed towards a coil at rest. Due to this induced electromotive force, induced current and induced charge in the coil is E, I, and Q respectively. If the speed of the magnet is doubled, the incorrect statement is:

A metallic ring connected to a rod oscillates freely like a pendulum. If now a magnetic field is applied in the horizontal direction so that the pendulum now swings through the field, the pendulum will: