- 1(current)
Q. No.Two magnetic dipoles, \(X\) and \(Y,\) are separated by a distance \(d,\) with their axes oriented perpendicular to each other. The dipole moment of \(Y\) is twice that of \(X.\) A charged particle with charge \(q\) moves with velocity \(v\) through their midpoint \(P,\) which makes an angle \(\theta=45^\circ\) with the horizontal axis, as shown in the diagram. Assuming \(d\) is much larger than the dimensions of the dipoles, the magnitude of the force acting on the charged particle at this instant is:
| 1. | \( 0 \) | 2. | \(\left(\dfrac{\mu_0}{4 \pi}\right) \dfrac{M}{\left(\dfrac{d}{2}\right)^3} \times q v \) |
| 3. | \(\sqrt{2}\left(\dfrac{\mu_0}{4 \pi}\right) \dfrac{M}{\left(\dfrac{d}{2}\right)^3} \times q v \) | 4. | \(\left(\dfrac{\mu_0}{4 \pi}\right) \dfrac{2 M}{\left(\dfrac{d}{2}\right)^3} \times q v\) |
| 1. | \(285~\text{A/m}\) | 2. | \(2600~\text{A/m}\) |
| 3. | \(520~\text{A/m}\) | 4. | \(1200~\text{A/m}\) |
A small bar magnet is placed in a uniform external magnetic field of magnitude \(0.06\text{ T},\) such that its magnetic axis makes an angle of \(30^\circ\) with the field. If the magnet experiences a torque of \(0.018\text{ N-m},\) what is the minimum work required to rotate the magnet from its stable equilibrium position to its unstable equilibrium position?
1. \(7.2\times 10^{-2}~\text{J}\)
2. \(11.7\times 10^{-3}~\text{J}\)
3. \(9.2\times 10^{-3}~\text{J}\)
4. \(6.4\times 10^{-2}~\text{J}\)
1. \(14~\text{J}\)
2. \(8.4~\text{J}\)
3. \(4~\text{J}\)
4. \(1.4~\text{J}\)
1. 2 : 1
2. 8 : 3
3. 1 : 3
4. 27 : 16
1. \(1~\text J\)
2. \(2~\text J\)
3. \(3~\text J\)
4. \(4~\text J\)
| 1. | \(3 \over 2\) | 2. | \(2 \over 3\) |
| 3. | \(4 \over 9\) | 4. | \(9 \over 4\) |
- 1(current)
Q. No.
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