Q. No.
A positive charge \(Q\) is uniformly distributed along a circular ring of radius \(R\). A small test charge \(q\) is placed at the centre of the ring. Then,
(a)
if \(q>0\) and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre.
(b)
if \(q<0\) and is displaced away from the centre in the plane of the ring, it will never return to the centre and will continue moving till it hits the ring.
(c)
if \(q<0\), it will perform SHM for small displacement along the axis.
(d)
q at the centre of the ring is in an unstable equilibrium within the plane of the ring for \(q>0\).
Choose the correct statement(s):
1. (a), (b), (c)
2. (a), (c), (d)
3. (b), (c), (d)
4. (c), (d)
Refer to the arrangement of charges in the figure and a Gaussian surface of a radius \(R\) with \(Q\) at the centre. Then:
| (a) | total flux through the surface of the sphere is \(\frac{-Q}{\varepsilon_0}.\) |
| (b) | field on the surface of the sphere is \(\frac{-Q}{4\pi \varepsilon_0 R^2}.\) |
| (c) | flux through the surface of the sphere due to \(5Q\) is zero. |
| (d) | field on the surface of the sphere due to \(-2Q\) is the same everywhere. |
Choose the correct statement(s):
| 1. | (a) and (d) | 2. | (a) and (c) |
| 3. | (b) and (d) | 4. | (c) and (d) |
| (a) | the electric field is necessarily zero. |
| (b) | the electric field is due to the dipole moment of the charge distribution only. |
| (c) | the dominant electric field is \(\propto \dfrac 1 {r^3}\), for large \(r\), where \(r\) is the distance from the origin in this region. |
| (d) | the work done to move a charged particle along a closed path, away from the region, will be zero. |
Which of the above statements are true?
1. (b) and (d)
2. (a) and (c)
3. (b) and (c)
4. (c) and (d)
| (a) | \(\oint_s {E} . {dS} \neq 0\) on any surface |
| (b) | \(\oint_s {E} . {dS} = 0\) if the charge is outside the surface. |
| (c) | \(\oint_s {E} . {dS}\) could not be defined. |
| (d) | \(\oint_s {E} . {dS}=\frac{q}{\epsilon_0}\) if charges of magnitude \(q\) were inside the surface. |
| 1. | (a) and (d) | 2. | (a) and (c) |
| 3. | (b) and (d) | 4. | (c) and (d) |
In the figure given below, two positive charges \(q_2\) and \(q_3\) fixed along the \(y\)-axis, exert a net electric force in the \(+x\text-\)direction on a charge \(q_1\) fixed along the \(x\)-axis. If a positive charge \(Q\) is added at \((x, 0),\) the force on \(q_1\):
| 1. | shall increase along the positive \(x\)-axis. |
| 2. | shall decrease along the positive \(x\)-axis. |
| 3. | shall point along the negative \(x\)-axis. |
| 4. | shall increase but the direction changes because of the intersection of \(Q\) with \(q_2\) and \(q_3\). |
A point positive charge is brought near an isolated conducting sphere (figure). The electric field is best given by:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
The electric flux through the surface:
| 1. | in figure-(iv) is the largest |
| 2. | in figure-(iii) is the least |
| 3. | in figure-(ii) is same as figure-(iii) but is smaller than figure-(iv) |
| 4. | is the same for all the figures |
Five charges \(q_1, q_2, q_3, q_4~\text{and}~q_5\) are fixed at their positions as shown in the figure, \(S\) is a Gaussian surface. The Gauss' law is given by \(\int_{S}E\cdot dS= \frac{q}{\varepsilon_0}\). Which of the following statements is correct?
| 1. | \(E\) on the LHS of the above equation will have contribution from \(q_1, q_5~\text{and}~q_3\) while \(q\) on the RHS will have a contribution from \(q_2~\text{and}~q_4\) only. |
| 2. | \(E\) on the LHS of the above equation will have a contribution from all charges while \(q\) on the RHS will have a contribution from \(q_2~\text{and}~q_4\) only. |
| 3. | \(E\) on the LHS of the above equation will have a contribution from all charges while \(q\) on the RHS will have a contribution from \(q_1, q_3~\text{and}~q_5\) only. |
| 4. | Both \(E\) on the LHS and \(q\) on the RHS will have contributions from \(q_2\) and \(q_4\) only. |
The figure shows electric field lines in which an electric dipole \(p\) is placed as shown in the figure. Which of the following statements is correct?
| 1. | The dipole will not experience any force. |
| 2. | The dipole will experience a force towards the right. |
| 3. | The dipole will experience a force towards the left. |
| 4. | The dipole will experience a force upwards. |
A point charge \(+q\) is placed at a distance \(d\) from an isolated conducting plane. The field at a point \(P\) on the other side of the plane is:
| 1. | directed perpendicular to the plane and away from the plane. |
| 2. | directed perpendicular to the plane but towards the plane. |
| 3. | directed radially away from the point charge. |
| 4. | directed radially towards the point charge. |
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