Question

The electric field of a charge q at a distance d away is measured as e. What will the electric field measure at a distance 1/2d away from the charge?

Answer 1

We are told the initial conditions:

$E= \frac{kq}{d^2}$

If we were to modify this equation and substitute 1/2d into d, we get:

$E = \frac{k*q}{(0.5d)^2}$

Simplifying this we get:

$E = 4[ \frac{kq}{d^2} ]$

This is 4 times our initial condition, so the answer is:

4E

Hope this helps!