(a) State Lanz'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 a expression for the mutual inductance of two long coaxial solenoids but having different radii and different number of turns.

Explanation

### Solution:

**(a) State Lenz's Law and Provide an Example:**

Lenz's Law states that "the direction of the induced current in a closed circuit is always such that it opposes the cause that produced it." This means that if a magnetic field is changing within a closed loop, the induced current will flow in a direction that creates its own magnetic field opposing the change.

**Example:**
Consider a scenario where we have a bar magnet with its north pole approaching a coil of wire. According to Lenz's Law, as the north pole of the magnet approaches the coil, the induced current in the coil will flow in such a way that it creates a north pole facing the approaching magnet. This opposition is a direct consequence of Lenz's Law.
...