Q. No.Which one of the following gives the value of the magnetic field according to Biot-Savart’s law?
1.
\(\frac{{i} \Delta {l} \sin (\theta)}{{r}^2} \)
2.
\(\frac{\mu_0}{4 \pi} \frac{i \Delta {l} \sin (\theta)}{r} \)
3.
\(\frac{\mu_0}{4 \pi} \frac{{i} \Delta{l} \sin (\theta)}{{r}^2} \)
4.
\(\frac{\mu_0}{4 \pi} {i} \Delta {l} \sin (\theta)\)
What is the magnetic field at point \(O\) in the figure?
1. \(\frac{\mu_{0} I}{4 \pi r}\)
2. \(\frac{\mu_{0} I}{4 \pi r} + \frac{\mu_{0} I}{2 \pi r}\)
3. \(\frac{\mu_{0} I}{4 r} + \frac{\mu_{0} I}{4 \pi r}\)
4. \(\frac{\mu_{0} I}{4 r} - \frac{\mu_{0} I}{4 \pi r}\)
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2. |  |
| 3. |  |
4. |  |
A current-carrying wire is placed in a uniform magnetic field in the shape of the curve \(y= \alpha \sin \left({\pi x \over L}\right),~0 \le x \le2L\)
. What will be the force acting on the wire?
| 1. | \(iBL \over \pi\) | 2. | \(iBL \pi\) |
| 3. | \(2iBL \) | 4. | zero |
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2. |  |
| 3. |  |
4. |  |
A particle of charge \(+q\) and mass \(m\) moving under the influence of a uniform electric field \(E\hat i\) and a uniform magnetic field \(B\hat k\) follows a trajectory from \(P\) to \(Q\) as shown in the figure. The velocities at \(P\) and \(Q\) are \(v\hat i\) and \(-2v\hat j\) respectively. Which of the following statement(s) is/are correct?
| 1. | \(E=\frac{3}{4} \frac{{mv}^2}{{qa}}\). |
| 2. | Rate of work done by electric field at \(P\) is \(\frac{3}{4} \frac{{mv}^3}{a}\). |
| 3. | Rate of work done by both fields at \(Q\) is zero. |
| 4. | All of the above. |
A particle with charge \(q\), moving with a momentum \(p\), enters a uniform magnetic field normally. The magnetic field has magnitude \(B\) and is confined to a region of width \(d\), where \(d< \frac{p}{Bq}.\) The particle is deflected by an angle \(\theta\) in crossing the field, then:
| 1. | \(\sin \theta=\frac{Bqd}{p}\) | 2. | \(\sin \theta=\frac{p}{Bqd}\) |
| 3. | \(\sin \theta=\frac{Bp}{qd}\) | 4. | \(\sin \theta=\frac{pd}{Bq}\) |
| 1. | attract each other with a force per unit length of \(\frac{\mu_0 i^2}{2\pi d^2}\). |
| 2. | repel each other with a force per unit length of \(\frac{\mu_0 i^2}{2\pi d^2}\). |
| 3. | attract each other with a force per unit length of \(\frac{\mu_0 i^2}{2\pi d}\). |
| 4. | repel each other with a force per unit length of \(\frac{\mu_0 i^2}{2\pi d}\). |
| 1. | \(\frac{1}{2}\) | 2. | \(1\) |
| 3. | \(4\) | 4. | \(\frac{1}{4}\) |
| 1. | \( \frac{\mu_0 i}{2 \sqrt{2} R} \) | 2. | \( \frac{\mu_0 i}{2 R} \) |
| 3. | \( \frac{\mu_0 i}{4 R} \) | 4. | \( \frac{\mu_0 i}{\sqrt{2} R}\) |
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