The magnetic flux through a circuit of resistance \(R\) changes by an amount \(\Delta \phi\) in time \(\Delta t\), Then the total quantity of electric charge \(Q\), which passing during this time through any point of the circuit is given by: 
1. \(Q= \frac{\Delta\phi}{\Delta t}\)
2. \(Q= \frac{\Delta\phi}{\Delta t} \times R\)
3. \(Q= -\frac{\Delta\phi}{\Delta t} + R\)
4. \(Q = \frac{\Delta \phi}{R}\)

A metallic ring is attached to the wall of a room. When the north pole of a magnet is brought near to it, the induced current in the ring will be:

A coil having an area A₀ is placed in a magnetic field which changes from B₀ to 4B₀ in a time interval t. The e.m.f. induced in the coil will be 

(1) $\frac{3A_0{B}_0}{t}$

(2) $\frac{4A_0{B}_0}{t}$

(3) $\frac{3B_0}{A_{0}t}$

(4) $\frac{4B_0}{A_{0}t}$

A copper ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet while it is passing through the ring is-

(1) Equal to that due to gravity

(2) Less than that due to gravity

(3) More than that due to gravity

(4) Depends on the diameter of the ring and the length of the magnet

A magnet is brought towards a coil (i) speedily (ii) slowly then the induced e.m.f./induced charge will be respectively 

(1) More in first case / More in the first case

(2) More in first case/Equal in both case

(3) Less in first case/More in second case

(4) Less in first case/Equal in both case

As shown in the figure, a magnet is moved with 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 

(1) E increases

(2) I increases

(3) Q remains the same

(4) Q increases

A coil having 500 square loops each of the side 10 cm is placed normal to a magnetic field which increases at the rate of 1.0 tesla/second. The induced e.m.f. in volts is 

(1) 0.1

(2) 0.5

(3) 1

(4) 5

When a magnet is pushed in and out of a circular coil C connected to a very sensitive galvanometer G as shown in the adjoining diagram with a frequency v, then

(1) Constant deflection is observed in the galvanometer

(2) Visible small oscillations will be observed in the galvanometer if v is about 50 Hz

(3) Oscillations in the deflection will be observed clearly if v = 1 or 2 Hz

(4) No variation in the deflection will be seen if v = 1 or 2 Hz

The magnetic field in a coil of 100 turns and 40 square cm area is increased from 1 Tesla to 6 Tesla in 2 second. The magnetic field is perpendicular to the coil. The e.m.f. generated in it is 

(1) 10⁴ V

(2) 1.2 V

(3) 1.0 V

(4) 10^–2 V

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

(1) Keep oscillating with the old-time period

(2) Keep oscillating with a smaller time period

(3) Keep oscillating with a larger time period

(4) Come to rest very soon