Question

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of -0.2071 N when separated by 50 cm, center-to-center. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.1165 N. What were the initial charges on the spheres? Since one is negative and you cannot tell which is positive or negative, there are two solutions. Take the absolute value of the charges and enter each value.

Answer 1

first , let the charges be q1 and -q2

so F = 9x10⁹ q1q2 / d²

0.2071 = 9x10⁹ q1q2 / 0.5²

hence q1q2 = 5.75 x 10^-12 ........ (1)

after removing the wire let the charges be Q1 and Q2

since they were connected by a conductor their potential differences are equal , and because they're identical then Q1 = Q2 = Q

so , 0.1165 = 9x10⁹ x Q² / 0.5²

Q1 = Q2 = 1.798 uC

so

Q1 + Q2 = 2Q

= 3.597 uC

= q1 + q2

q2 = 3.597uC +q1

from eq 1:

q1q2 = 5.75 x 10^-12

q1 (3.597uC + q1) = 5.75 x 10^-12
q1=1.1989*10^-12 and 4.795*10^-12