Physics

Problem

Which expression gives the electric potential

V

at a distance

r

from an isolated point charge

q

in vacuum? a)

V=\dfrac{1}{2}\,k_{e}\,\dfrac{q}{r}

V = 4\pi\,k_{e}\,\dfrac{q}{r}

V = k_{e}\,\dfrac{q}{r}

V = -\,k_{e}\,\dfrac{q}{r}

Intuitive explanation

The key insight is that electric potential measures the energy per unit charge needed to bring a test charge from infinity to a point in space. For a point charge, the potential depends only on how far away you are—the closer you get, the more work you've done against the electric field. The relationship follows an inverse-distance pattern, just like the electric field itself, but without the test charge in the denominator.

Intuitive explanation

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