Two geometrically identical spheres with electric charges Q and 3Q are separated by a distance of r in a vacuum. The electrostatic force between them is 48 µN. The two spheres are brought into contact and then separated to the former distance. Determine the magnitude of the force that each sphere now experiences.

###### Solution. Posted on Friday, May 15, 2015.

The Coulomb’s law F = k*q1*q2/r^2 , where q1 – the charge of the object 1, q2 – the charge of the object 2, r – distance between the centers of the two objects, k – the Coulomb Constant 9*10^9 N*m^2/C^2 and F – the magnitude of the electrostatic force between two electric charges.

According to the law of conservation of charge, the spheres have a total charge of 4Q and it is divided equally between two geometrically identical spheres.

Hence, the initial force Fi = k*Q*3Q/r^2 and the final force Ff = k*2Q*2Q/r^2.

Finally, Ff = 4/3 * Fi = 4/3*48 = 64 µN.