Electrostatics Question 236

Question: A charge +q is fixed at each of the points x=x0,x=3x0,x=5x0 ….. infinite, on the x axis and a charge q is fixed at each of the points x=2x0,x=4x0,x=6x0 ,….. infinite. Here x0 is a positive constant. Take the electric potential at a point due to a charge Q at a distance r from it to be Q/(4πε0r) . Then, the potential at the origin due to the above system of charges is [IIT 1998]

Options:

A) Electric field near A in the cavity = Electric field near B in the cavity

B) Charge density at A= Charge density at B

C) Potential at A= Potential at B

D) Total electric field flux through the surface of the cavity is q/ε0

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Answer:

Correct Answer: C , D

Solution:

Under electrostatic condition, all points lying on the conductor are in same potential. Therefore, potential at A = potential at B.

From Gauss’s theorem, total flux through the surface of the cavity will be q/ε0 .

Not: q Instead of an elliptical cavity, if it would had been a spherical cavity then options (a) and (b) were also correct.

Under electrostatic condition, all points lying on the conductor are in same potential. Therefore, potential at A = potential at B.

From Gauss’s theorem, total flux through the surface of the cavity will be q/ε0 .



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