The electric potential at a distance $d$ from a point charge is $\mathrm{V}$. At a distance $\mathrm{d}$ ', the potential is $2 \mathrm{~V}$. What is the ratio of electric field at $\mathrm{d}$ to that at $\mathrm{d}$ ?

Question

Quizplus · Accepted Answer

The electric field is the negative gradient of the electric potential. So, the ratio of electric fields is equal to the ratio of the negative gradients of the electric potentials. The negative gradient of the electric potential at a distance $d$ is $-dV/dr$, and the negative gradient of the electric potential at a distance $d'$ is $-2dV/dr$. Therefore, the ratio of electric fields is $-dV/dr$ / $-2dV/dr$ = 1 / 2.

The Electric Potential at a Distance ddd From a Point Charge Is

The Electric Potential at a Distance $d$ From a Point Charge Is