Question

Two point charges totaling 7.00 µC exert a repulsive force of 0.250 N on one another when separated by 0.357 m. What is the charge (in µC) on each?

smallest charge

largest charge

(b) What is the charge (in µC) on each if the force is attractive?

smallest charge

largest charge

Answer 1

given total charge Q = q1 + q2 = 7*10^-6 C

q2 = 7*10^-6 - q1

force of repulsion F = 0.25 N

r = 0.357 m

force of repulsion F = k*q1*q2/r^2

k*q1*q2/r^2 = 0.25

9*10^9*q1(7*10^-6 - q1)/0.357^2 = 0.25

q1(7*10^-6 - q1) = 3.54*10^-12

q1*7*10^-6 - q1^2 = 3.54*10^-12

q1 = 0.55*10^-6 C <<<<<--------ANSWER

q2 = 7*10^-6 - 6.45*10^-6

q2 = 6.45*10^-6 N <<<<--------ANSWER

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(b)

if force is attractive

q1 + q2 = 7*10^-6 N

q2 = 7*10^-6 - q2

force of repulsion F = -0.25 N

r = 0.357 m

force of repulsion F = k*q1*q2/r^2

k*q1*q2/r^2 = -0.25

9*10^9*q1(7*10^-6 - q1)/0.357^2 = -0.25

q1(7*10^-6 - q1) = -3.54*10^-12

q1*7*10^-6 - q1^2 = -3.54*10^-12

q1 = -0.474*10^-6 C <<<<<--------ANSWER

q2 = 7*10^-6 -(-0.474*10^-6)

q2 = 7.474*10^-6 C    <<<<<--------ANSWER