Q. No.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. |
A hemisphere is uniformly charged positively. The electric field at a point on a diameter away from the centre is directed:
| 1. | perpendicular to the diameter. |
| 2. | parallel to the diameter. |
| 3. | at an angle tilted towards the diameter. |
| 4. | at an angle tilted away from the diameter. |
If \(\int_S E.ds = 0\) over a surface, then:
| (a) | the electric field inside the surface and on it is zero. |
| (b) | the electric field inside the surface is necessarily uniform. |
| (c) | the number of flux lines entering the surface must be equal to the number of flux lines leaving it. |
| (d) | all charges must necessarily be outside the surface. |
Choose the correct statement(s):
| 1. | (a), (c) |
| 2. | (b), (c) |
| 3. | (c), (d) |
| 4. | (a), (d) |
| (a) | always continuous. |
| (b) | continuous if there is no charge at that point. |
| (c) | discontinuous only if there is a negative charge at that point. |
| (d) | discontinuous if there is a charge at that point. |
Choose the correct option:
| 1. | (a), (b) | 2. | (b), (d) |
| 3. | (c), (d) | 4. | (a), (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) |
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