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 \(1.6\times10^{-4}\) m2, carrying a current of \(4.0\) A, is suspended through its center allowing it to turn in a horizontal plane. The magnetic moment associated with the solenoid is:
1. \(0.18\) Am2
2. \(3.24\) Am2
3. \(1.28\) Am2
4. \(0.38\) Am2
| 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. | \({i}_{0}\left({{4}\mathit{\pi}{R}_{0}}\right) \) |
© 2024 GoodEd Technologies Pvt. Ltd.