The electric field a distance rA from a positively charged point charge is equal to EA. What is the ratio EB to EA of the electric field at point B a distance of 3rA from the charge?
A) EB = 1/9 EA
B) EB = 1/3 EA
C) EB = 3EA
D) EB = 9EA
This question asks the examinee to determine the ratio of the electric field due to a point charge as a function of distance. The electric field of a point charge is given by the following equation:
E = kq/r2
Therefore, the ratio of the electric field at point B to point A is equal to:
EB / EA = (kq/rB2) / (kq/rA2) = rA2 / rB2 = rA2 / 9rA2 = 1/9
Thus, EB = 1/ 9 EA making A the correct answer.