Question

Two small plastic spheres are given positive electrical charges. When they are 16.0 cm apart, the repulsive force between them has magnitude 0.200 N.
a)What is the charge on each sphere if the two charges are equal?

b)What is the charge on each sphere if one sphere has four times the charge of the other?

Answer 1

Answer:

a) 7.5425 * 10^-7 C

b) 3.7712 * 10^-7 C ; 1.5085 * 10^-6 C

Explanation:

Part a)

$F_{elect} = \frac{k*q_{1}*q_{2} }{R^2} \\q_{1} = q_{2} = q\\q = \sqrt{\frac{F_{elect} * R^2}{k} }\\ = \sqrt{\frac{0.2 * 0.16^2}{9*10^9} }\\\\ q = 7.5425 * 10 ^(-7) C$

Part b)

$F_{elect} = \frac{k*q_{1}*q_{2} }{R^2} \\q_{1} = 4*q_{2} \\q = \sqrt{\frac{F_{elect} * R^2}{k*4} }\\ = \sqrt{\frac{0.2 * 0.16^2}{4*9*10^9} }\\\\ q_{2} = 3.7712 * 10 ^(-7) C\\\\q_{1} = 1.5085 * 10 ^(-6) C$