A circular loop carrying a current is replaced by an equivalent magnetic dipole. A point on the axis of the loop is in:
1. | end-on position | 2. | broadside-on position |
3. | both | 4. | none |
a. | P1 and P2 |
b. | Q1 and Q2 |
c. | P1 and Q1 |
d. | P2 and Q2 |
Choose the correct option:
1. (a), (b)
2. (b), (c)
3. (c), (d)
4. (a), (d)
When a bar magnet is rotated from its position parallel to the external magnetic field \(B=10^{-3}\) T to a direction opposite to the field (anti-parallel), the work done is \(3\) J.
Then, the maximum torque experienced by this magnet in this field is:
1. \(3\times10^{-3}\) N-m
2. \(3\times10^{3}\) N-m
3. \(6\) N-m
4. \(1.5\) N-m
1. | \(\dfrac{\pi}{\mu_0}\left(B_eR^3\right )\) | 2. | \(\dfrac{2\pi}{\mu_0}\left(B_eR^3\right )\) |
3. | \(\dfrac{4\pi}{\mu_0}\left(B_eR^3\right )\) | 4. | \(\dfrac{2}{\mu_0}\left(B_eR^3\right )\) |
Three identical bar magnets, each having dipole moment \(M,\) are placed at the origin — oriented along the x-axis, the y-axis and the z-axis respectively. The net magnetic moment of the dipoles has the magnitude:
1. \(3M\)
2. \(\sqrt2M\)
3. \(\sqrt3M\)
4. zero
1. | \(\frac{MB}{F}\) | 2. | \(\frac{BF}{M}\) |
3. | \(\frac{MF}{B}\) | 4. | \(\frac{F}{MB}\) |
The following figures show the arrangement of bar magnets in different configurations. Each magnet has a magnetic dipole. Which configuration has the highest net magnetic dipole moment?
1. | 2. | ||
3. | 4. |
1. | \(B^{-3}\) | 2. | \(B^{-2}\) |
3. | \(B^{-1/2}\) | 4. | \(B^{-1/3}\) |
1. \(\frac{\mu_{\mathrm{0}}}{4 \pi} \frac{\mathrm{M}}{\mathrm{d}^{3}}\)
2. \(\frac{\mu_{0}}{4 \pi} \frac{\sqrt{2} \mathrm{M}}{\mathrm{d}^{3}}\)
3. \(\frac{\mu_{0}}{4 \pi} \frac{2\sqrt{2} \mathrm{M}}{\mathrm{d}^{3}}\)
4. \(\frac{\mu_{\mathrm{0}}}{4 \pi} \frac{\mathrm{2M}}{\mathrm{d}^{3}}\)
1. | \(6 \times 10^{-4}\) T | 2. | \(1.5 \times 10^{-4}\) T |
3. | \(3 \sqrt2 \times 10^{-4}\) T | 4. | \({\dfrac 3 {\sqrt 2}}\times 10^{-4}\) T |