Question

(a) State Lenz’s law. Give one example to illustrate this law. “The Lenz’s law is a consequence of the principle of conservation of energy.” Justify this statement. 

(b) Deduce an expression for the mutual inductance of two long co-axial solenoids but having different radii and different number of turns.

Answer 1

(a) Lenz's law: According to this law “the direction of induced current in a closed circuit is always such as to oppose the cause that produces it.” Example: When the north pole of a coil is brought near a closed coil, the direction of current induced in the coil is such as to oppose the approach of north pole. For this the nearer face of coil behaves as north pole. This necessitates an anticlockwise current in the coil, when seen from the magnet side [fig. (a)]

Similarly when north pole of the magnet is moved away from the coil, the direction of current in the coil will be such as to attract the magnet. For this the nearer face of coil behaves as south pole. This necessitates a clockwise current in the coil, when seen from the magnet side (fig. b). 

Conservation of Energy in Lenz’s Law: Thus, in each case whenever there is a relative motion between a coil and the magnet, a force begins to act which opposes the relative motion. Therefore to maintain the relative motion, a mechanical work must be done. This work appears in the form of electric energy of coil. Thus Lenz’s law is based on conservation of energy. 

(b) Suppose two co-axial solenoids S₁  and S₂  of radii r₁  and r₂ , number of turns N₁  and N₂ each of length ‘l’ 

Suppose I₁  is the current in outer solenoid; magnetic field at the axis, B₁ = m where n₁ = μ₀n₁I₁ number of turns/meter of outer solenoid. 

Magnetic flux linked with inner solenoid (S₂).