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. | \(R \over 2\) |