The ratio of the radii of two circular coils is \(1:2\). The ratio of currents in the respective coils such that the same magnetic moment is produced at the centre of each coil is:
1. \(4:1\)
2. \(2:1\)
3. \(1:2\)
4. \(1:4\)

A uniform conducting wire of length \(12a\) and resistance '\(R\)' is wound up as a current carrying coil in the shape of,
(i) an equilateral triangle of side '\(a\)'
(ii) a square of side '\(a\)'
The magnetic dipole moments of the coil in each case respectively are:
1. \(3Ia^2~\text{and}~4Ia^2\)
2. \(4Ia^2~\text{and}~3Ia^2\)
3. \(\sqrt{3}Ia^2~\text{and}~3Ia^2\)
4. \(3Ia^2~\text{and}~Ia^2\)

A wire of length \(L\) meters carrying a current of \(I\) amp is bent in the form of a circle. What is its magnetic moment?
1. \( \frac{{IL}^2}{4} ~\text{A}\text-\text{m}^2 \)
2. \( \frac{{I} \times \pi {L}^2}{4} ~\text{A}\text-\text{m}^2 \)
3. \( \frac{2 {IL}^2}{\pi}~\text{A}\text-\text{m}^2 \)
4. \( \frac{{IL}^2}{4 \pi}~\text{A}\text-\text{m}^2 \)