Q. No.1. \(\dfrac{x}{8}\)
2. \(\dfrac{x}{4}\)
3. \(\dfrac{x}{2}\)
4. \(2x\)
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. \(\dfrac{{IL}^{2}}{{4}\mathit{\pi}}\)
2. \(\dfrac{IL}{{4}\mathit{\pi}}\)
3. \(\dfrac{{I}^{2}L}{{4}\mathit{\pi}}\)
4. \(\dfrac{{I}^{2}{L}^{2}}{{4}\mathit{\pi}}\)
A \(100\) turn closely wound circular coil of radius \(10~\text{cm}\) carries a current of \(3.2~\text{A}.\) The magnetic moment of this coil is:
1. \(20~\text{A-m}^2\)
2. \(10~\text{A-m}^2\)
3. \(30~\text{A-m}^2\)
4. \(15~\text{A-m}^2\)
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. \( \dfrac{{IL}^2}{4 \pi}~\text{A}\text-\text{m}^2 \)
| 1. | \(\dfrac{q^2\phi}{2m}\) | 2. | \(\dfrac{q^2\phi}{2\pi m}\) |
| 3. | \(\dfrac{q^2\phi}{m}\) | 4. | \(\dfrac{q^2\phi}{\pi m}\) |
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 closely wound solenoid of \(2000\) turns and area of cross-section as \(1.6\times10^{-4}~\text m^2,\) carrying a current of \(4.0~\text A,\) is suspended through its center allowing it to turn in a horizontal plane. The magnetic moment associated with the solenoid is:
1. \(0.18~\text{Am}^2\)
2. \(3.24~\text{Am}^2\)
3. \(1.28~\text{Am}^2\)
4. \(0.38~\text{Am}^2\)
| 1. | The magnitude of the magnetic moment now diminishes. |
| 2. | The magnetic moment does not change. |
| 3. | The magnitude of B at (0, 0, z), z >>R increases. |
| 4. | The magnitude of B at (0, 0, z), z >>R is unchanged. |
| 1. | \(\left({{i}_{0}\mathit{\pi}{R}_{0}^{2}}\right)\sqrt{2} \) | 2. | zero |
| 3. | \({i}_{0}\times{2}\mathit{\pi}{R}_{0}^{2} \) | 4. | \({i}_{0}\left({{4}\mathit{\pi}{R}_{0}}\right) \) |
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