In each case given below, point charges are fixed in place. The potential at infinity is taken as zero.
(a) Charges \(+q\) and \(-q\) are at the two ends of a line. O is the midpoint of the line.
(b) Charges \(+q\), \(-q\), \(+q\) and \(-q\) are at the corners A, B, C and D of a square, in that order. O is the centre of the square.
(c) A charge \(+q\) is at each corner of a square. O is the centre of the square.
(d) Charges \(+2q\) and \(-q\) are at the two ends of a line. O is the midpoint of the line.
(e) Charge \(+2q\) is at A and charge \(-q\) is at B, with AB = 3 cm. O is on AB, 2 cm from A.
(f) A thin spherical shell carries a charge \(+q\) spread uniformly over it. O is the centre of the shell.
(g) Charges \(+q\) and \(-q\) are at points A and B. O is on the line AB, beyond B.
In how many of these cases is the electric potential at O zero?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Three
Potential is a scalar. The potential at a point is the algebraic sum of the potentials of all the charges, each with its own sign. It is zero only when the positive and negative parts balance.
The cases in which the potential at O is zero:
(a) — zero, \( +q \) and \( -q \) are at equal distances from O
(b) — zero, the charges at A and C balance those at B and D
(e) — zero, \( 2q/2 \) from A balances \( q/1 \) from B (distances in cm)
The cases in which it is not:
(c) — all four terms are positive, so they add
(d) — equal distances but unequal charges, so the potential is positive
(f) — the field inside the shell is zero, but the potential equals its surface value
(g) — O is nearer to \( -q \), so the potential is negative
Number of cases with zero potential at O = 3
NCERT (2026-27):
Potential Due to a System of Charges – “… By the superposition principle, the potential V at P due to the total charge configuration is the algebraic sum of the potentials due to the individual charges”
\( V=V_1+V_2+\dots+V_n \qquad (2.17) \)
Potential Due to an Electric Dipole – “… The potential in the equatorial plane (θ = π/2) is zero.”
Example 2.4 – “… The electrostatic potential at E is clearly zero since potential due to A and C is cancelled by that due to B and D. …”
Potential Due to a System of Charges – “… The electric field inside the shell is zero. This implies … that potential is constant inside the shell (as no work is done in moving a charge inside the shell), and, therefore, equals its value at the surface, which is”
\( V=\frac{1}{4\pi\varepsilon_0}\frac{q}{R} \qquad [2.19(b)] \)