(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 \(q>0\). |
Refer to the arrangement of charges in the figure and a Gaussian surface of radius \(R\) with \(Q\) at the centre. Then:
(a) | total flux through the surface of the sphere is \(\dfrac{-Q}{\varepsilon_0}\). |
(b) | field on the surface of the sphere is \(\dfrac{-Q}{4\pi \varepsilon_0 R^2}.\) |
(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) | on any surface. |
(b) | if the charge is outside the surface. |
(c) | could not be defined. |
(d) | if charges of magnitude \(q\) were inside the surface. |
In the figure, 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. 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. |