Two particles each of mass \(m\) and charge \(q\) are attached to the two ends of a light rigid rod of length \(2R\). The rod is rotated at constant angular speed about a perpendicular axis passing through its centre.
What is the ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod?
1. \(\frac{q}{2m}\)
2. \(\frac{q}{m}\)
3. \(\frac{2q}{m}\)
4. \(\frac{q}{\pi m}\)
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. | 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 \(2 \pi \times 10^{-5}~\text{N/m}\) |
a. | \(\vec{B}\) should be perpendicular to the direction of velocity and \(\vec{E}\) should be along the direction of velocity. |
b. | Both \(\vec{B}\) and \(\vec{E}\) should be along the direction of velocity. |
c. | Both \(\vec{B}\) and \(\vec{E}\) are mutually perpendicular and perpendicular to the direction of velocity. |
d. | \(\vec{B}\) should be along the direction of velocity and \(\vec{E}\) should be perpendicular to the direction of velocity. |
Which one of the following pairs of statements are possible?
1. (a) and (c)
2. (c) and (d)
3. (b) and (c)
4. (b) and (d)
1. | \(R \over 3\) | 2. | \(\sqrt{3}R\) |
3. | \(R \over \sqrt3\) | 4. | \(R \over 2\) |
What happens when the number of turns in a galvanometer is doubled?
1. | voltage sensitivity becomes double. |
2. | current sensitivity becomes double. |
3. | voltage sensitivity becomes half. |
4. | current sensitivity remains the same. |
The two parts of the loop are circles of radii \(2a\) and \(a\), respectively, and carry the same current \(i\) as shown in the given figure. What is the magnitude of the dipole moment of the current loop?
1. \(5 \pi a^{2}\) \(i\)
2. \(4 \pi a^{2}\) \(i\)
3. \(3 \pi a^{2}\) \(i\)
4. zero
What is the magnetic moment of the following current loop?
1. \(24~\text{Am}^2\)
2. \(12~\text{Am}^2\)
3. \(6~\text{Am}^2\)
4. zero
1. \(\mu_{0} i_{1} i_{2}\)
2. \(\frac{\mu_{0} i_{1} i_{2}}{\pi}\)
3. \(\frac{\mu_{0} i_{1} i_{2}}{2 \pi}\)
4. \(2 \mu_{0} i_{1} i_{2}\)