A small square loop of wire of side l is placed inside a large square of wire of side L (L>>l). The loops are co-planar and their centres coincide. The mutual inductance of the system is proportional to :

1. l/L

2. ${\mathrm{l}}^2/\mathrm{L}$

3. L/l

4. ${\mathrm{L}}^2/\mathrm{l}$

 

The key \(K\) is inserted at time \(t=0\). The initial \((t=0)\) and final \(t\rightarrow \infty\) currents through the battery are:
                              

1. \(\frac{1}{15}~\text{A},~\frac{1}{10}~\text{A}\)
2. \(\frac{1}{10}~\text{A},~\frac{1}{15}~\text{A}\)
3. \(\frac{2}{15}~\text{A},~\frac{1}{10}~\text{A}\)
4. \(\frac{1}{15}~\text{A},~\frac{2}{25}~\text{A}\)

Two coils have a mutual inductance of 5 mH. Current changes in the first coil according to the equation I = $I_0$cos wt, where $I_0$ = 10 A and $\mathrm{\omega } = 100\mathrm{\pi }$ rad/s. Maximum value of e.m.f. induced in the second coil is

1.  5$\pi$ volt

2.   2$\pi$ volt

3.  4$\pi$ volt

4.  $\pi$ volt

Lenz's law is a consequence of the law of conservation of 

(1) Charge

(2) Momentum

(3) Mass

(4) Energy

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