Question

Problem 22.32

PART A

By what distance do two objects carrying 1.0 C of charge each have to be separated before the electric force exerted on each object is 8.0 N ?

PART B

How much charge should be placed on each of two small objects separated by 2.5 m so that the electric force exerted on each is 8.0 N ?

Answer 1

Electrostatic force is given by:

F = k*q1*q2/R^2

Given that: q1 = q2 = 1.0 C

R = distance between charges = ?

F = Force exerted = 8.0 N

So,

R^2 = k*q1*q2/F

R = sqrt (k*q1*q2/F)

R = sqrt (9*10^9*1.0*1.0/8.0) = 33541 m

R = distance between both charges = 3.35*10^4 m = 33.5 km

Part B.

F = k*q1*q2/R^2

Given that: q1 = q2 = ? C (Suppose q)

R = distance between charges = 2.5

F = Force exerted = 8.0 N

So,

F = k*q*q/R^2

q^2 = F*R^2/k

q = sqrt (F*R^2/k)

q = sqrt (8.0*2.5^2/(9*10^9)) = 74.5*10^-6 C

q = Charge on each object = 74.5*10^-6 C = 74.5 C

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