Q. No.A particle of mass \(m,\) charge \(Q,\) and kinetic energy \(T\) enters a transverse uniform magnetic field of induction \(\vec B.\) What will be the kinetic energy of the particle after seconds?
| 1. | \(3{T}\) | 2. | \(2{T}\) |
| 3. | \({T}\) | 4. | \(4{T}\) |
| 1. | \(8\) N in \(-z\text-\)direction. |
| 2. | \(4\) N in the \(z\text-\)direction. |
| 3. | \(8\) N in the \(y\text-\)direction. |
| 4. | \(8\) N in the \(z\text-\)direction. |
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. |
A beam of electrons passes un-deflected through mutually perpendicular electric and magnetic fields. Where do the electrons move if the electric field is switched off and the same magnetic field is maintained?
| 1. | in an elliptical orbit. |
| 2. | in a circular orbit. |
| 3. | along a parabolic path. |
| 4. | along a straight line. |
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 |
| 1. | \(1~\text{GHz}\) | 2. | \(100~\text{MHz}\) |
| 3. | \(62.8~\text{MHz}\) | 4. | \(6.28~\text{MHz}\) |
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 neutron, a proton, an electron and an \(\alpha\text-\)particle enter a region of the uniform magnetic field with the same velocity. The magnetic field is perpendicular and directed into the plane of the paper. The tracks of the particles are labelled in the figure.
Which track will the \(\alpha\text-\)particle follow?
| 1. | \(A\) | 2. | \(B\) |
| 3. | \(C\) | 4. | \(D\) |
A charged particle is projected through a region in a gravity-free space. If it passes through the region with constant speed, then the region may have:
1. \(\vec{E}=0, \vec{B} \neq 0\)
2. \(\vec{E} \neq 0, \vec{B} \neq 0\)
3. \(\vec{E} \neq 0, \vec{B}=0\)
4. Both (1) & (2)
| a. | \(\vec{B}\) should be perpendicular to the direction of velocity and \(\vec{E}\) should be along the direction of velocity. |
| b. | Both \(\vec{B}\) and \(\vec{E}\) should be along the direction of velocity. |
| c. | Both \(\vec{B}\) and \(\vec{E}\) are mutually perpendicular and perpendicular to the direction of velocity. |
| d. | \(\vec{B}\) should be along the direction of velocity and \(\vec{E}\) should be perpendicular to the direction of velocity. |
Which one of the following pairs of statements are possible?
1. (a) and (c)
2. (c) and (d)
3. (b) and (c)
4. (b) and (d)
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