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: Recall what magnetic moment means.
A flat coil carrying current behaves like a tiny magnet. The strength of this equivalent magnet is measured by its magnetic (dipole) moment, \(m = NIA\), where \(N=1\) for a single rectangular loop.

Step 2: Convert the dimensions into SI units.
Length \(= 20\text{ cm} = 0.20\text{ m}\) and breadth \(= 10\text{ cm} = 0.10\text{ m}\).

Step 3: Compute the enclosed area.
\(A = \text{length} \times \text{breadth} = 0.20 \times 0.10 = 2 \times 10^{-2}\ \text{m}^2\).

Step 4: Plug into the formula.
With \(I = 10\ \text{A}\),
\(m = (1)(10)(2\times 10^{-2}) = 20 \times 10^{-2}\ \text{A}\cdot\text{m}^2\).

Step 5: Simplify.
\(m = 0.2\ \text{A}\cdot\text{m}^2\), directed normal to the coil plane.

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