Q. No.A current loop consists of two identical semicircular parts each of radius \(R,\) one lying in the \(x\text-y\) plane, and the other in the \(x\text-z\) plane. If the current in the loop is \(i,\) what will be the resultant magnetic field due to the two semicircular parts at their common centre?
1.
\( \dfrac{\mu_0 i}{2 \sqrt{2} R} \)
2.
\( \dfrac{\mu_0 i}{2 R} \)
3.
\( \dfrac{\mu_0 i}{4 R} \)
4.
\( \dfrac{\mu_0 i}{\sqrt{2} R}\)
| 1. | \(\frac{1}{2}\) | 2. | \(1\) |
| 3. | \(4\) | 4. | \(\frac{1}{4}\) |
| 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 \(\frac{\mu_0 i^2}{2\pi d}\). |
A current \(I\) is carried by an elastic circular wire of length \(L\). It is placed in a uniform magnetic field \(B\) (out of paper) with its plane perpendicular to \(B'\text{s}\) direction. What will happen to the wire?
| 1. | No force | 2. | A stretching force |
| 3. | A compressive force | 4. | A torque |
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. | \(\sin \theta=\frac{pd}{Bq}\) |
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 \(\mathrm B\hat k\) 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. |
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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 |
A particle of charge \(q\) and mass \(m\) is moving along the \(x\text-\)axis with a velocity of \(v\) and enters a region of electric field \(E\) and magnetic field \(\mathrm B\) as shown in the figure below. For which figure is the net force on the charge zero?
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