Match the position of point P in List-I with the electric potential at P in List-II. All charges are point charges and \(k=\frac{1}{4\pi\varepsilon_0}\).
| List-I | List-II |
|---|---|
| (A) P is midway between charges \(+q\) and \(+q\) placed \(2r\) apart | (I) Zero |
| (B) P is midway between charges \(+q\) and \(-q\) placed \(2r\) apart | (II) \(kq/r\) |
| (C) P is the centre of a square with a charge \(+q\) at each corner; each corner is at distance \(r\) from P | (III) \(2kq/r\) |
| (D) P is at distance \(r\) from a charge \(+2q\) and at distance \(2r\) from a charge \(-2q\) | (IV) \(4kq/r\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
Potential is a scalar. The potential at P due to a group of charges is the algebraic sum of the potentials \( kq_i/r_i \) of the separate charges. Each is taken with its sign.
(A) P is midway between charges \( +q \) and \( +q \) placed \( 2r \) apart — This matches (III) \( 2kq/r \). Each charge is at distance \( r \) from P and adds \( kq/r \).
(B) P is midway between charges \( +q \) and \( -q \) placed \( 2r \) apart — This matches (I) zero. The two terms are \( +kq/r \) and \( -kq/r \), so their sum is zero.
(C) P is the centre of a square with a charge \( +q \) at each corner — This matches (IV) \( 4kq/r \). All four charges are positive and at the same distance \( r \), so each adds \( kq/r \). The four fields add to zero at the centre, but the potentials do not, because potential has no direction.
(D) P is at distance \( r \) from \( +2q \) and at distance \( 2r \) from \( -2q \) — This matches (II) \( kq/r \). The charge \( +2q \) gives \( 2kq/r \) and the charge \( -2q \) gives \( -kq/r \). Their sum is \( kq/r \).
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”
\( V=V_1+V_2+\dots+V_n \qquad (2.17) \)