Two identical conducting spheres, fixed in place, attract each other with an ele

Question

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of -0.9321 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 the smaller value here.

Explanation / Answer

F = K Q1 Q2 / R^2.

Solve this once, for product Q1 Q2 using -0.6786.

Solve this again, for product (Q1+dq) (Q2-dq) using 0.1165.

You'll have 2 equations, 2 unknowns. A bit of algebra, and perhaps solving a quadratic, and you'll be able to find dq, the change in charge.

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