Consider two uniformaly charged concentric and coaxial rings of radii R and 2R. Total charge on inner ring is `Q_(1)` and that on outer ring is `Q_(2)`. Both rings are revolving in same sence with same angular velocity about its axis. If net magnetic induction at a distance R feom the centre of the rings, on axis of rings is zero then `(Q_(1))/(Q_(2))` is :

Options

A. `-1`
B. `-(2sqrt(2))/(5sqrt(5))`
C. `-(8sqrt(2))/(5sqrt(5))`
D. `-(4sqrt(2))/(3sqrt(3))`

Explanation

To solve the problem, we need to find the ratio of the charges on the two concentric rings when the net magnetic induction at a distance \( R \) from the center of the rings is zero.

### Step-by-Step Solution:

1. **Understanding the Magnetic Field Due to a Ring**:
The magnetic field \( B \) at a distance \( x \) along the axis of a ring of radius \( R \) carrying a current \( I \) is given by the formula:
\[
B = \frac{\mu_0}{4\pi} \cdot \frac{2I R^2}{(R^2 + x^2)^{3/2}}
...