Question

A charge of 2.308 nC is moved from a position on the y axis of 5.423 cm to a position on the x axis of 1.356 cm while there is a charge 17.119 nC located at the origin. How much work in micro-Joules did it take to move the charge?

Answer 1

We are asked to determine the work done to move a charge from location A to location B as shown in the following diagram:

The work done is the change in the potential electric energy of the system, that is:

`W=U_b-U_a`

The electric energy is given by:

`U=k(q_1q_2)/(r)`

Substituting we get:

`W=k(q_1q_2)/(R_b)-k(q_1q_2)/(R_a)`

Taking common factors:

`W=kq_1q_2((1)/(R_b)-(1)/(R_a))`

Now, we plug in the values:

`W=(9*10{}{}^9(Nm^2)/(C^2))(2.308*10^(-9)C)(17.119*10^(-9)C)((1)/(0.01356m)-(1)/(0.05423m))`

Solving the operations:

`W=3.28*10^(-5)J`

This is equivalent to:

`W=32.8\mu J`

Therefore, the work required is 32.8 micro joules.