Question

Regarding the distance dependence of quantities due to a point charge, which of the following is correct?

Options

• Force \[F \propto \frac{1}{r^2}\], electric field \[E \propto \frac{1}{r^2}\], potential \[V \propto \frac{1}{r}\]

• Force \[F\], electric field \[E\], and potential \[V\] all vary as \[\frac{1}{r}\]

• Force \[F \propto \frac{1}{r}\], electric field \[E \propto \frac{1}{r^2}\], potential \[V \propto \frac{1}{r^2}\]

• Force \[F \propto \frac{1}{r^2}\], electric field \[E \propto \frac{1}{r}\], potential \[V \propto \frac{1}{r^2}\]

Answer 1

For a point charge, the force and electric field both follow an inverse-square dependence \[F \propto \frac{1}{r^2}\], \[E \propto \frac{1}{r^2}\], while the potential follows an inverse-first-power dependence \[V \propto \frac{1}{r}\]. This is because potential is the integral of the field over distance.