Five charges q1, q2, q3, q4, and q5

Question:
Five charges q₁, q₂, q₃, q₄, and q₅ are fixed at their positions as shown in Fig. 1.4. S is a Gaussian surface.

The Gauss’s law is given by

Which of the following statements is correct?

(a) E on the LHS of the above equation will have a contribution from q₁, q₅and q₃ while q on the RHS will have a contribution from q₂ and q₄ only.

(b) 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.

(c) 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.

(d) Both E on the LHS and q on the RHS will have contributions from q₂ and q₄ only.

Solution:

According to Gauss' theorem, the term q on the right side of the equation includes the sum of all charges enclosed by the surface (irrespective of the position of the charges inside the surface).

If the surface is so chosen that there are some charges inside and some outside, the electric field on the left side of equation will be due to all charges (both inside and outside)

Here, E on LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from charges q₂ and q₄ only.

Five charges q1, q2, q3, q4, and q5

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