Question

A total charge of 3.98 C is distributed on two metal spheres. When the spheres are 10.00 cm apart, they each feel a repulsive force of 4.4*10^11 N. How much charge is on the sphere which has the lower amount of charge

Answer 1

Let the charges on the spheres be q1 and q2

q1 + q2 = 3.98

or

q1 = 3.98 - q2

and

$k q_1 q_2/r^2 = 4.4\times 10^{11}$

r = 10 cm= 0.1 m

k = 8.99 x 10^9

or

$8.99\times 10^9 (3.98-q_2) q_2/0.1^2 = 4.4\times 10^{11}$

or

(3.98 – 92)2 = 0.489

$3.98q_2-q_2^2-0.489=0$

or

$q_2^2-3.98q_2+0.489=0$

solving this quadratic equation gives

$q_2=0.127\,C$

and

$q_2=3.853\,C$

therefore the charge is on the sphere which has the lower amount of charge is

q2 = 3.853 C