A coil in the shape of an equilateral triangle of side 0.02 m is suspended from a vertex such that it is hanging in a vertical plane between the pole pieces of a permanent magnet producing a horizontal magnetic field of `5 xx 10^(-2) T.` Find the couple acting on the coil when a current of 0.1 A is passed through it and the magnetic field is parallel to its plane.

Explanation

To solve the problem, we need to calculate the couple (torque) acting on a coil in the shape of an equilateral triangle when a current passes through it in a magnetic field. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Geometry and Parameters
We have an equilateral triangle coil with a side length of \( a = 0.02 \, \text{m} \). The magnetic field \( B = 5 \times 10^{-2} \, \text{T} \) is horizontal and parallel to the plane of the coil. The current flowing through the coil is \( I = 0.1 \, \text{A} \).

**Hint:** Remember that the area of an equilateral triangle can be calculated using the formula \( A = \frac{\sqrt{3}}{4} a^2 \).

### Step 2: Calculate the Area of the Coil
...