Question

Imagine a scenario where two positive point charges Q₁ and Q₂ are present in space at points A and B respectively. The electric potential at infinity is assumed to be zero. The electric potential at a finite point P is observed to be zero, then;
1. Another positive charge except Q1 and Q2 must exist in space.
2. Another negative charge except Q1 and Q2 must exist in space.
3. Another positive and negative charge except Q1 and Q2 must exist in space.
4. No other charge except Q1 and Q2 exists in space.

Answer 1

Correct Answer - Option 2 : Another negative charge except Q1 and Q2 must exist in space.

CONCEPT:

• Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

\(⇒ V=\frac{W}{q}\)

• Potential due to a single charged particle Q at a distance r from it is given by:

\(⇒ V=\frac{Q}{4\piϵ_{0}r}\)

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

• Potential at a point P due to a system of charged particles Q1, Q2, Q3, ... Qn having distances r1, r2, r3, ... rn respectively from point P is given by:

\(⇒ V=\frac{Q_1}{4\piϵ_{0}r} + \frac{Q_2}{4\piϵ_{0}r} + \frac{Q_3}{4\piϵ_{0}r} + ...+\frac{Q_n}{4\piϵ_{0}r}\)

\(⇒ V=\sum_{i=1}^{n}\frac{Q_i}{4\piϵ_{0}r_i}\)

EXPLANATION:

• The total potential due to the two existing charges Q1 and Q2 at point P.

\(\Rightarrow V = V_1 + V_2 = \frac{Q_1}{4\pi \epsilon _0 r_1} + \frac{Q_2}{4\pi \epsilon _0 r_2}\)

• Since Q1, Q2, r₁, and r₂ are all positive constants, the total potential at V can have a zero value only if another charge exists in space such that,

\(\Rightarrow V_{total} = 0 = V_1 + V_2 +V_3 = \frac{Q_1}{4\pi \epsilon _0 r_1} + \frac{Q_2}{4\pi \epsilon _0 r_2}+ \frac{Q_3}{4\pi \epsilon _0 r_3}\)

• Since Q1, Q2, r1, r2, and r3 are all positive constants, the total potential at V can have a zero value only Q₃ has a negative value. Therefore option 2 is correct.