Two insulated rings, one of a slightly smaller diameter than the other, are suspended along their common diameter as shown. Initially, the planes of the rings are mutually perpendicular. What happens when a steady current is set up in each of them?
1. | the two rings rotate into a common plane. |
2. | the inner ring oscillates about its initial position. |
3. | the inner ring stays stationary while the outer one moves into the plane of the inner ring. |
4. | the outer ring stays stationary while the inner one moves into the plane of the outer ring. |
A charge \(Q\) is uniformly distributed on a ring of radius \(R\) made of an insulating material. If the ring rotates about the axis passing through its centre and normal to the plane of the ring with constant angular speed \(\omega\), then what will be the magnitude of the magnetic moment of the ring?
1. \(Q \omega R^{2}\)
2. \(\frac{1}{2} Q \omega R^{2}\)
3. \(Q \omega^{2} R\)
4. \(\frac{1}{2} Q\omega^{2} R\)
1. | \(10^{-5} ~\text{N} \), attractive |
2. | \(10^{-5}~\text{N} \), repulsive |
3. | \(2 \times 10^{-5}~\text{N} \), attractive |
4. | \(2 \times 10^{-5} ~\text{N} \), repulsive |
1. | Repulsive force of \(10^{-4}~\text{N/m}\) |
2. | Attractive force of \(10^{-4}~\text{N/m}\) |
3. | Repulsive force of \(2 \pi \times 10^{-5}~\text{N/m}\) |
4. | Attractive force of \(2 \pi \times 10^{-5}~\text{N/m}\) |
An alternating electric field of frequency \(\nu\), is applied across the dees (radius=R) of a cyclotron that is being used to accelerate protons(mass=m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by:
1. \(\mathrm{B}=\frac{m \nu}{\mathrm{e}}\) and \(K=2 m \pi^{2} \mathrm{\nu}^{2} \mathrm{R}^{2}\)
2.\(\mathrm{B}=\frac{2\pi m \nu}{\mathrm{e}}\) and \(K=m^2 \pi \mathrm{\nu} \mathrm{R}^{2}\)
3. \(\mathrm{B}=\frac{2\pi m \nu}{\mathrm{e}}\) and \(K=2 m \pi^{2} \mathrm{\nu}^{2} \mathrm{R}^{2}\)
4. \(\mathrm{B}=\frac{m \nu}{\mathrm{e}}\) and \(K=m^2 \pi \mathrm{\nu} \mathrm{R}^{2}\)
1. | putting in series resistance of \(240 ~\Omega \text {. }\) |
2. | putting in parallel resistance of \(240 ~\Omega \text {. }\) |
3. | putting in series resistance of \(15~ \Omega \text {. }\) |
4. | putting in parallel resistance of \(15~ \Omega \text {. }\) |
1. | \(nB\) | 2. | \(n^2B\) |
3. | \(2nB\) | 4. | \(2n^2B\) |
1. | infinite | 2. | zero |
3. | \( \frac{\mu_0 2 i}{4 \pi} ~\text{T} \) | 4. | \( \frac{\mu_0 i}{2 r} ~\text{T} \) |
1. | \(R \over 3\) | 2. | \(\sqrt{3}R\) |
3. | \(R \over \sqrt3\) | 4. | \(R \over 2\) |