Question

How electric field is related to the distance between two charge ($r$) particle?

• A. Directly proportional to $r$
• B. Directly proportional to $r^2$
• C. Inversely proportional to $r$
• D. Inversely proportional to $r^2$

Answer 1

The correct option is D Inversely proportional to $r^2$

Let two charges $q$ and $q_0$ (+ive test charge) are placed at a distance $r$ from each other.

Force experienced by charge $q_0$ is $F$, then electric field at the point, where $q_0$ is placed

$E=\frac{F}{q_0}$ ...............eq1

Now, the force between $q$ and $q_0$, by Coulomb's law

$F=k\frac{q{q}_0}{r^2}$

Putting the value of $F$ in eq1,

$E=k\frac{q}{r_2}$

$E\propto 1/r^2$