A rectangular coil of N turns, with each turn of length 6 cm and breadth 8 cm is suspended freely in a magnetic field of strength 90 G. The field lines are in the plane of the coil. The torsional constant of the hair springs connected to the coil is ` 3 xx 10^(-9)` Nm/deg and a current of ` 5 muA` through the coil deflects it through on angle of `20^(@)` . What is the value of N?

Explanation

To solve the problem, we need to find the number of turns \( N \) in a rectangular coil that is suspended in a magnetic field. We will use the relationship between torque, current, magnetic field, and the properties of the coil.

### Step 1: Calculate the area of one turn of the coil
The area \( A \) of one turn of the rectangular coil can be calculated using the formula:
\[ A = \text{length} \times \text{breadth} \]
Given that the length is \( 6 \, \text{cm} = 0.06 \, \text{m} \) and the breadth is \( 8 \, \text{cm} = 0.08 \, \text{m} \):
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