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

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

1. Charge

2. Momentum

3. Mass

4. Energy

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 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 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

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

An aluminum ring B faces an electromagnet A. The current I through A can be altered. Then :

1. Whether I increases or decreases, B will not experience any force

2. If I decrease, A will repel B

3. If I increases, A will attract B

4. If I increases, A will repel B

Two rails of a railway track insulated from each other and the ground are connected to a milli voltmeter. What is the reading of voltmeter, when a train travels with a speed of \(180\) km/hr along the track.
(Given that the vertical component of earth's magnetic field is \(0.2\times 10^{-4}\) weber/m² and the rails are separated by \(1\) m) 
1. \(10^{-2}\) V
2. \(10^{-4}\) V
3. \(10^{-3}\) V
4. \(1\) V

A conducting square loop of side \(L\) and resistance \(R\) moves in its plane with a uniform velocity \(v\) perpendicular to one of its sides. A magnetic induction \(B\) constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere. The current induced in the loop is: