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
Subtopic:  Gauss's Law |
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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 ${\int }_{\mathbf{S}}\mathbf{E}.\mathrm{d}\mathbf{S}=\frac{\mathrm{q}}{{\mathrm{\epsilon }}_{0}}$. 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.

Subtopic:  Gauss's Law |
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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.

1. (a, c)
2. (b, c)
3. (c, d)
4. (a, d)

Subtopic:  Gauss's Law |
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If there were only one type of charge in the universe, then,

 1 ${\oint }_{s}E.dS\ne 0$ on any surface. 2 ${\oint }_{s}E.dS=0$ if the charge is outside the surface. 3 ${\oint }_{s}E.dS$ could not be defined. 4 ${\oint }_{s}E.\mathrm{dS}=\frac{q}{{\epsilon }_{0}}$ if charges of magnitude q were inside the surface.
Choose the correct statement(s):
1. a and d
2. a and c
3. b and d
4. c and d
Subtopic:  Gauss's Law |
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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 $\propto \frac{1}{{r}^{3}},$ 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

Subtopic:  Gauss's Law |
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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 $\frac{-\mathrm{Q}}{{\epsilon }_{0}}$. b. field on the surface of the sphere is $\frac{-Q}{4\pi {\epsilon }_{0}{R}^{2}}$. 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

Subtopic:  Gauss's Law |
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