Find the mutual inductance of two concentric coils of radii `a_(1)` and `a_(2)(a_(1) lt lt a_(2))` if the planes of the coils are perpendicular.

Explanation

To find the mutual inductance of two concentric coils of radii \( a_1 \) and \( a_2 \) (where \( a_1 \ll a_2 \)) with their planes perpendicular, we can follow these steps:

### Step 1: Understand the Setup
We have two concentric coils. The inner coil has a radius \( a_1 \) and the outer coil has a radius \( a_2 \). The planes of the coils are perpendicular to each other.

### Step 2: Determine the Magnetic Field
When a current \( I \) flows through the outer coil (with radius \( a_2 \)), it generates a magnetic field at the center of the coil. The magnetic field \( B \) at the center of a circular coil is given by the formula:
\[
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