Question

Assume we are given an electric field set up by an unknown charge distribution. U0 is the amount of work needed to bring a point charge of charge q0 in from infinity to a point P. If the charge q0 is returned to infinity, how much work would it take to bring a new charge of 4 q0 from infinity to point P?

Answer 1

Answer:

$4U_0$

Explanation:

We are given that

Amount of work needed to bring a point charge q0 from infinity to a point P=$U_0$

We know that potential at point P=$V=\frac{U}{q}$

$U=Vq$

Where U=Amount of work needed to bring a point charge q from infinity to a point P

Initially ,$V=\frac{U_0}{q_0}$

New charge, q=$4q_0$

Then, work done,U=$\frac{U_0}{q_0}\times (4q_0)=4U_0$

Hence, the amount of  work needed to bring a new charge 4q0 from infinity to point P=$4U_0$