of the charge Q initially on a sphere ,a portion q is to be transferred to a second, nearby sphere, - Physics - Electric Charges And Fields

Question

of the charge Q initially on a sphere ,a portion q is to be
transferred to a second, nearby sphere, Both spheres can be treated
as particles For what value of q/Q will the electrostatic force
between the two spheres be maxised?

Somnath physics · Accepted Answer

Let â€˜râ€™ be the distance between the two spheres When â€˜qâ€™ charge is transferred, the charges on the spheres are (Q-q) and q So, electrostatic force is,

Differentiation F w r t q and setting it to zero will give us the extremum force

For this value of q/Q the force is extremum (minimum or maximum) The force will be maximum if the second differentiation of F is less than zero

Thus, the required value of q/Q is 1/2

of the charge Q initially on a sphere ,a portion q is to be transferred to a second, nearby sphere, Both spheres can be treated as particles .For what value of q/Q will the electrostatic force between the two spheres be maxised?