Correct Answer - Option 2 : Another negative charge except Q

1 and Q

2 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, r
_{1}, and r_{2} 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 Q**_{3} has a negative value. Therefore option 2 is correct.