Question

A charge q produces an electric field of strength 2E at a distance of d away. Determine the electric field strength at a distance of 1/2d away.

Answer 1

The electric field strength of a point charge is inversely proportional to the square of the distance from the charge ... a lot like gravity.

If the magnitude of the field is (2E) at the distance 'd', then at the distance '2d', it'll be (2E)/(2²).  That's (2E)/4 = 0.5E .

Answer 2

Answer:

8 E

Explanation:

The formula for the electric field at point P which is at a distance r from the charge Q due to the charge Q is given by

E = k Q / r^2

If a charge is at a distance d from the charge q, the electric field is given by

2E = k q / d^2    .... (1)

Let the electric field at a distance 1/2 d is E'

E' = k q / (d/2)^2

E' = 4 k q / d^2 = 4 x 2E   (From equation (1)

E' = 8 E