A point charge q is located at the origin. A charge q0 can be placed at a point P1, which is a distance r from the origin (top drawing). Or, a charge 2q0 can be placed at P2, which is a distance 2r from the origin (bottom drawing). All charges are positive. Which statement is true about the electric potentials due charge q at P1 and P2?

a. The electric potential at P1 is greater than that at P2, because r is smaller than 2r.
b. The electric potential at P1 is the same as that at P2.
c. The electric potential at P1 is less than that at P2, because q0 is smaller than 2q0.
d. The electric potential at P1 is less than that at P2, because r is smaller than 2r.

Option A is correct

The electric potential at P1 is greater than that at P2, because r is smaller than 2r.

Explanation:

Electric potential at a point due to a particular charge (q) at r distance from that point is given as

V = kQ/r

where k = Coulomb's constant

For point P₁, the electric potential due to charge q, r distance away is given as

V₁ = kq/r

For point P₂, the electric potential due to charge q, (2r) distance away is given as

V₂ = kq/(2r)

This shows that the electric potential due to charge q at P1 is twice that experienced at P2 because of the same charge.

The electric potential at a point due to a particular only depends on the charge in question and the distance of that charge from that point.

If the charge and other parameters are constant, the electric potential at some distance away is inversely proportional to that distance. So, smaller r, indicates bigger electric potential.