If there were only one type of charge in the universe, then,
1. | on any surface. |
2. | if the charge is outside the surface. |
3. | could not be defined. |
4. | if charges of magnitude q were inside the surface. |
Consider a region inside where there are various types of charges but the total charge is zero. At points outside the region:
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 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 radius R with Q at the centre. Then:
a. | total flux through the surface of the sphere is . |
b. | field on the surface of the sphere is . |
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 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. |
1. (a, b, c)
2. (a, c, d)
3. (b, c, d)
4. (c, d)
The electric field at a point on the equatorial plane at a distance \(r\) from the centre of a dipole having dipole moment \(\overrightarrow{P}\) is given by:
(\(r\gg\) separation of two charges forming the dipole, \(\epsilon_{0} =\) permittivity of free space)
1. \(\overrightarrow{E}=\frac{\overrightarrow{P}}{4\pi \epsilon _{0}r^{3}}\)
2. \(\overrightarrow{E}=\frac{2\overrightarrow{P}}{\pi \epsilon _{0}r^{3}}\)
3. \(\overrightarrow{E}=-\frac{\overrightarrow{P}}{4\pi \epsilon _{0}r^{2}}\)
4. \(\overrightarrow{E}=-\frac{\overrightarrow{P}}{4\pi \epsilon _{0}r^{3}}\)
The acceleration of an electron due to the mutual attraction between the electron and a proton when they are \(1.6~\mathring{A}\) apart is:
( \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9~ \text{Nm}^2 \text{C}^{-2}\) )
1. | \( 10^{24} ~\text{m/s}^2\) | 2 | \( 10^{23} ~\text{m/s}^2\) |
3. | \( 10^{22}~\text{m/s}^2\) | 4. | \( 10^{25} ~\text{m/s}^2\) |
In the figure, two positive charges q2 and q3 fixed along the y-axis, exert a net electric force in the +x-direction on a charge q1 fixed along the x-axis. If a positive charge Q is added at (x, 0), the force on q1
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 q2 and q3.
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 q1, q2, q3, q4, and q5 are fixed at their positions as shown in the figure, S is a Gaussian surface. The Gauss' law is given by . Which of the following statements is correct?
1. | E on the LHS of the above equation will have contribution from q1, q5 and q3 while q on the RHS will have a contribution from q2 and q4 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 q2 and q4 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 q1, q3 and q5 only. |
4. | Both E on the LHS and q on the RHS will have contributions from q2 and q4 only. |