Centers of two similar coils P and Q having same number of turns are located at the coordinates (0.4,0) and (0,0.3) such that the plane of coils are perpendicular to X-and Y-axis respectively. The areas of cross section of coils P and Q are in the ration `4:3` Coil P has 16 A current in clockwise direction and coil Q has `9sqrt3A` current in anticlockwise direction as seen from the origin. A small compass needle is placed at the origin. Find the deflection in the needle, assuming the earth's magnetic field negligible and the radii of the coils very small compared to their distances from the origin.

Explanation

To solve the problem step by step, we will calculate the magnetic fields produced by coils P and Q at the origin, then find the deflection of the compass needle based on the ratio of these magnetic fields.

### Step 1: Identify the magnetic field due to coil P
The magnetic field \( B_P \) at the origin due to coil P can be calculated using the formula:
\[ B_P = \frac{\mu_0 N I_P A_P}{2 \pi X_P^3} \]
Where:
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