A point charge of 2Q0 is located at y a How much work is re

A point charge of +2Q_0 is located at y = +a. How much work is required to bring a second charge of -3Q_0 from infinity to y = -a? How much work is required to bring a third charge of +4Q_0 from infinity to the origin? How much work is required to move tire +4Q_0 from the origin to the point y = +2? For nil three parts, please express your energy as u rational number limes U_0, whose value is (Q_0^2/4 pi epsilon_o a).

Solution

The work done to put a charge Q at a point with potential U is given as: qU

We will make use of the above to solve the given problems as follows:

Part a.) The potential at point y = -a due to the charge +2Q at y= +a would be given as:

U = k2Q/2a = kQo/a

Now the work done to bring -3Qo from infinity would be charge x potential = -3kQo²/ a = -3Uo

Part b.) Now, we have two charges in the vicinity of the origin, therefore the net potential at the origin will be the sum of the potentials due to each one of them

Potential at origin = -3kQo / a + 2kQo/a = -kQo/a

Hence the work done to bring +4Qo to origin would be =Charge x potential

Work done = -4kQo²/a = -4Uo.

Part c.) Potential at y = +2a would be sum of potentials due to each of the three charges in its vicinity

Potentia at y = +2a is given as: U = 2kQo/a + 4kQo / 2a - 3kQo/3a = 3kQo/a

Therefore work done to bring +4Qo from infinity to y = +2a would be given as:

Work done = Charge x potential = 12kQo²/a = 12 Uo