Two point charges of magnitude +q and -q are separated by a distance 2r. The electric potential at the mid point of the two charges is:

CONCEPT:

Electric Potential:

• The electric potential at a point in an electric field is defined as the amount of work done in moving a unit positive test charge from infinity to that point, without acceleration, against the electric force due to the electric field.

The electric potential at a point due to a point charge is given as,

\(⇒ V=\frac{kQ}{r}\)

Where Q = magnitude of a point charge, r = distance of a point from the charge, and k = 9×10⁹ N-m²/C²

CALCULATION:

Given Q₁ = +q and Q₂ = -q

• The midpoint of the two charges will be at a distance r from both the charges.
• So the electric potential at the midpoint due to charge +q is given as,

\(⇒ V_{1}=\frac{kq}{r}\)     -----(1)

And the electric potential at the midpoint due to charge -q is given as,

\(⇒ V_{2}=\frac{-kq}{r}\)     -----(2)

So the net electric potential at the midpoint is given as,

⇒ V = V₁ + V₂

\(⇒ V=\frac{kq}{r}-\frac{kq}{r}\)

⇒ V = 0

• Hence, option 1 is correct.