| 1. | \( \dfrac{{IL}^2}{4} ~\text{A}\text-\text{m}^2 \) | 2. | \( \dfrac{{I} \times \pi {L}^2}{4} ~\text{A}\text-\text{m}^2 \) |
| 3. | \( \dfrac{2 {IL}^2}{\pi}~\text{A}\text-\text{m}^2 \) | 4. | \( \dfrac{{IL}^2}{4 \pi}~\text{A}\text-\text{m}^2 \) |
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. \(3Ia^2~\text{and}~Ia^2\)
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. | \(1:4\) |
| 1. | \(\left({{i}_{0}{\pi}{R}_{0}^{2}}\right)\sqrt{2} \) | 2. | zero |
| 3. | \({i}_{0}\times{2}{\pi}{R}_{0}^{2} \) | 4. | \({i}_{0}\left({{4}{\pi}{R}_{0}}\right) \) |