Question

Find out the magnetic moment of a rectangular coil of size 20 cm × 10 cm having 10 A current.

Hint:

Use the magnetic moment of a current loop, \(m = NIA\), with area in square metres and one turn.

Answer 1

Step 1: Write the concept and formula.
The magnetic moment of a current-carrying coil is given by
\[ m = N\,I\,A \]
where \(N\) is the number of turns, \(I\) is the current, and \(A\) is the area of the coil. Here the coil is a single loop, so \(N = 1\).

Step 2: Find the area of the coil.
The sides are \(20\text{ cm} = 0.20\text{ m}\) and \(10\text{ cm} = 0.10\text{ m}\).
\[ A = 0.20 \times 0.10 = 0.02\ \text{m}^2 \]

Step 3: Substitute the values.
\[ m = 1 \times 10\ \text{A} \times 0.02\ \text{m}^2 \]

Step 4: Do the arithmetic.
\[ m = 0.2\ \text{A}\cdot\text{m}^2 \]
The direction of the magnetic moment is perpendicular to the plane of the coil, given by the right-hand rule.

\[\boxed{m = 0.2\ \text{A}\cdot\text{m}^2}\]