Two Questions (MCQ) on Electric Potential

(1) An infinite number of point charges each equal to +Q coulomb are arranged at random around a point P such that the distances of the charges from the point P are 1m, 2m, 4m, 8m, 16m,…….etc... The electric potential at P is

(a) zero (b) infinite (c) negligibly small

(d) Q/2πε₀ (e) Q/4πε₀

Note that the electric potential is a scalar quantity. Therefore, the direction of the location of the charge does not matter and the potentials simply add up. The resultant potential (V) at P is given by

V = (Q/4πε₀) × [(1/1) + (1/2) + (1/4) + (1/8) + ………]

The infinite series within the square bracket yields a value equal to 2 so that V = Q/2πε_0.

(2) A thin spherical conducting shell of radius R has a charge +Q. Another point charge –q is placed at the centre of the shell. The electrostatic potential at a point P distant R/2 from the centre of the shell is

(a) (Q/4πε₀R) – (2q/4πε₀R) (b) (q/4πε₀R) – (2Q/4πε₀R)

(c) – (2q/4πε₀R) (d) (Q/4πε₀R) (e) zero
The electrostatic potential at any point within the shell due to the charge Q on the shell is constant and is equal to Q/4πε₀R.

The potential at distance R/2 due to the charge –q placed at the centre of the shell is – q/4πε₀(R/2) = – 2q/4πε₀R.

Therefore, the net potential (V) at the point P distant R/2 from the centre of the shell is given by

V = (Q/4πε₀R) – (2q/4πε₀R), given in option (a).

[Note that positive charges will produce positive potential where as negative charges will produce negative potential].

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You will find similar multiple choice questions with solution at physicsplus also.