Question

Two identical conducting spheres, fixed in place, attract each
other with an electrostatic force of -0.5574 *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 0.0325
*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 the smaller value here.

Answer #1

**Let q1 and q2 are the initial charges on the
spheres.**

**F = k*q1*q2/d^2**

**-0.5574 = 9*10^9*q1*q2/0.5^2**

**==> q1*q2 = -0.5575*0.5^2/(9*10^9)**

**q1*q2 = -1.548*10^-11 ---(1)**

**when they are connected q1' = q2' =
(q1+q2)/2**

**F' = k*q1'*q2'/d^2**

**0.0325 = 9*10^9*( (q1+q2)/2)^2/0.5^2**

**((q1+q2)/2)^2 = 0.0325*0.5^2/(9*10^9)**

**q1+q2 = 2*sqrt(0.0325*0.5^2/(9*10^9) )**

**q1 + q2 = 1.9*10^-6 ---(2)**

**on solving the two equations**

**q1 = -3.1*10^-6 C and q2 = 5*10^-6 C**

**or**

**q1 = 5*10^-6 C and q2 = -3.1*10^-6 C**

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