Q. No.Two small paramagnetic samples are placed in an (otherwise uniform) strong external magnetic field \(B.\) If the two samples are placed with a separation that is along the direction of the external field \(B,\) then, the force exerted by the two samples on each other is:
1.
attractive.
2.
repulsive.
3.
zero.
4.
any of the above depending on the external field \(B\) and the sample separation.
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Which of the following, is independent of \(\theta?\)
| 1. | \(E_B\cdot\tau_B\) | 2. | \(\dfrac{E_B}{\tau_B}\) |
| 3. | \(E_B^2+\tau_B^2\) | 4. | \(E_B^2-\tau_B^2\) |
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| 1. | \(\dfrac{r_1}{r_2}=\dfrac{P_1}{P_2}\) |
| 2. | \(\left(\dfrac{r_1}{r_2}\right)^2=\dfrac{P_1}{P_2} \) |
| 3. | \(\left(\dfrac{r_1}{r_2}\right)^3=\dfrac{P_1}{P_2} \) |
| 4. | none of the above is true. |
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Now, the temperature of the sample is decreased. The magnetisation:
| 1. | increases |
| 2. | decreases |
| 3. | remains unchanged |
| 4. | decreases first and then increases |
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| 1. | \(B^{-3}\) | 2. | \(B^{-2}\) |
| 3. | \(B^{-1/2}\) | 4. | \(B^{-1/3}\) |
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| 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. | \(\dfrac{2}{\mu_0}\left(B_eR^3\right )\) |
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| 1. | force along +ve \(y\text-\)axis |
| 2. | force along -ve \(y\text-\)axis |
| 3. | zero force but a clockwise torque |
| 4. | zero force but an anticlockwise torque |
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| 1. | increased |
| 2. | decreased |
| 3. | unchanged |
| 4. | fluctuating with time: first increasing and then decreasing |
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1. \(3 \times 10^{-5}\) N-m
2. \(30\) N-m
3. \(3 \times 10^{-3}\) N-m
4. \(3 \times 10^{-2}\) N-m
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| 1. | \(0.75~\text{A}\) | 2. | \(75~\text{A}\) |
| 3. | \(1.33~\text{A}\) | 4. | \(133~\text{A}\) |
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