Q. No.The figure shows some of the electric field lines corresponding to an electric field. The figure suggests:
1. EA > EB > EC
2. EA = EB = EC
3. EA = EC > EB
4. EA = EC < EB
| (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) |
| (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)
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) | 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 \(q>0\). |
1. (a), (b), (c)
2. (a), (c), (d)
3. (b), (c), (d)
4. (c), (d)
1. \(\phi_E =\dfrac{q}{\epsilon_0}\)
2. \(\phi_E =\dfrac{2q}{\epsilon_0}\)
3. \(\phi_E =\dfrac{p}{\epsilon_0 r^2}\)
4. \(\phi_E = 0\)
A metallic spherical shell has an inner radius \(R_1\) and an outer radius \(R_2.\) A point charge \(Q\) is placed at the center of the spherical cavity. What are the surface charge densities \(\sigma_{in}\) and \(\sigma_{out}\) on the inner and outer surfaces of the shell, respectively?
1. \(\sigma_{in} = -\dfrac{Q}{4\pi R_1^2},~ \sigma_{out}=\dfrac{Q}{4\pi R_2^2}\)
2. \(\sigma_{in} = \dfrac{Q}{4\pi R_1^2},~ \sigma_{out}=0\)
3. \(\sigma_{in} = 0,~ \sigma_{out}=\dfrac{Q}{4\pi R_2^2}\)
4. \(\sigma_{in} = \dfrac{Q}{4\pi R_1^2},~ \sigma_{out}=-\dfrac{Q}{4\pi R_2^2}\)
| 1. |  |
| 2. |  |
| 3. |  |
| 4. |  |
What will be the total flux through the faces of the cube as given in the figure with a side of length 'a' if a charge q is placed at?
Match the following:
| Column I | Column II | ||
| (a) | a corner of the cube | (i) | \(\phi=\dfrac{q}{2\epsilon_0}\) |
| (b) | mid-point of an edge of the cube | (ii) | \(\phi=\dfrac{q}{8\epsilon_0}\) |
| (c) | centre of a face of the cube | (iii) | \(\phi=\dfrac{q}{2\epsilon_0}\) |
| (d) | mid-point of B and C | (iv) | \(\phi=\dfrac{q}{4\epsilon_0}\) |
| 1. | (A)\(\rightarrow \)(iv), (B)\(\rightarrow \)(ii), (C)\(\rightarrow \)(iii), (D)\(\rightarrow \)(i) |
| 2. | (A)\(\rightarrow \)(ii), (B)\(\rightarrow \)(iv), (C)\(\rightarrow \)(i), (D)\(\rightarrow \)(iii) |
| 3. | (A)\(\rightarrow \)(iii), (B)\(\rightarrow \)(ii), (C)\(\rightarrow \)(iv), (D)\(\rightarrow \)(i) |
| 4. | (A)\(\rightarrow \)(i), (B)\(\rightarrow \)(iii), (C)\(\rightarrow \)(ii), (D)\(\rightarrow \)(iv) |
A paisa coin is made up of \(Al-Mg\) alloy and weighs \(0.75~\text g.\) It has a square shape and its diagonal measures \(17~\text{mm}.\) It is electrically neutral and contains equal amounts of positive and negative charges. Treating the paisa coin as if it were made up of only Aluminum \(Al,\) find the magnitude of the equal number of positive and negative charges. What conclusion do you draw from this magnitude?
| 1. | \(3.48\times 10^4~\text C, \) everyday objects contain enormous amounts of charge |
| 2. | \(5.4\times 10^4~\text C, \) The net charge of neutral objects is always significant |
| 3. | \(1.34\times 10^4~\text C, \) The positive and negative charges in neutral objects perfectly cancel out |
| 4. | \(1.34\times 10^4~\text C, \) The amount of positive and negative charge in neutral objects is negligible |
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