In what orientation, the mutual inductance associated with given two circular coils kept with their centres at distance d is maximum.

Explanation

To determine the orientation in which the mutual inductance associated with two circular coils is maximum, we can follow these steps:

### Step 1: Understand Mutual Inductance
Mutual inductance is a measure of the ability of one coil to induce an electromotive force (emf) in another coil due to a change in current in the first coil. The mutual inductance \( M \) depends on the magnetic flux linking the second coil due to the current in the first coil.

### Step 2: Identify the Coils' Orientation
The orientation of the coils plays a crucial role in determining the amount of magnetic flux that passes through the second coil. For maximum mutual inductance, we need to ensure that the magnetic field produced by the first coil passes through the second coil effectively.

...