Question

The strength of the electric field at a certain distance from a point charge is represented by E. What is the strength of the electric field at twice the distance from the point charge?
a.) At twice the distance, the strength of the field is E/2.
b.) At twice the distance, the strength of the field is 2E.
c.)At twice the distance, the strength of the field is 4E.
d.)At twice the distance, the strength of the field remains equal to E.
e.)At twice the distance, the strength of the field is E/4.

Answer 1

Answer:

e.)At twice the distance, the strength of the field is E/4.

Explanation:

The strength of the electric field at a certain distance from a point charge is given by:

$E=k\frac{Q}{r^2}$

where

k is the Coulomb's constant

Q is the charge

r is the distance from the point charge

In this problem, the distance from the point charge is doubled:

r' = 2r

So the new electric field strength is

$E'=k\frac{Q}{(2r)^2}=k \frac{Q}{4 r^2}=\frac{1}{4} (k\frac{Q}{r^2})=\frac{E}{4}$

so, at twice the distance the strength of the field is E/4.