Question

(a) Two point charges totaling 7.50 µC exert a repulsive force of 0.150 N on one another when separated by 0.812 m. What is the charge (in µC) on each? smallest charge in µC largest charge in µC

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

Answer 1

(a) Consider the first condition, we have q1 + q2 = 7.50µC and that F = 0.150 N when r = 0.812 m

Now the expression for the force between the two charges is -

F = k*q1*q2/r^2

=> q1*q2 = F*r^2/k = 0.150 * 0.812^2/(9.0x10^9) = 11.0x10^-12

So we have, q1*(7.50x10^-6 - q1) = 11.0x10^-12

Expanding -q1^2 + 7.50x10^-6q1 - 11.0x10^-12 = 0

so q1 = (-7.50x10^-6 +- sqrt((7.50x10^-6)^2 - 4*(-1)*(-11.0x10^-12)))/(2*(-1)) = 2.0 x10^-6C

therefore, the other charge, q2 = 7.50x10^-6 - 2.0x10^-6 = 5.50x10^-6 C

(b) When the force is attractive, means the two charges are of the opposite sign.

so we have -

q1 - q2 = 7.50 µC and that F = 0.150 N when r = 0.812 m

write the expression for the force -

F = k*q1*q2/r^2

=> q1*q2 = F*r^2/k = 0.150*0.812^2/(9.0x10^9) = 11.0x10^-12

=> q1*(q1 - 7.50 x 10^-6) = 11.0x10^-12

Expanding q1^2 + 7.50x10^-6*q1 - 11.0x10^-12 = 0

so q1 = (-8.50x10^-6 +- sqrt((7.50x10^-6)^2 - 4*(1)*(-11.0x10^-12)))/(2*(1)) = 0.756x10^-6 C

And, q2 = q1 - 7.50 x 10^-6 = 0.756 x 10^-6 - 7.50x10^-6 = -6.74 x 10^-6 C