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:
[tex]W=U_b-U_a[/tex]The electric energy is given by:
[tex]U=k\frac{q_1q_2}{r}[/tex]Substituting we get:
[tex]W=k\frac{q_1q_2}{R_b}-k\frac{q_1q_2}{R_a}[/tex]Taking common factors:
[tex]W=kq_1q_2(\frac{1}{R_b}-\frac{1}{R_a})[/tex]Now, we plug in the values:
[tex]W=(9\times10{}{}^9\frac{Nm^2}{C^2})(2.308\times10^{-9}C)(17.119\times10^{-9}C)(\frac{1}{0.01356m}-\frac{1}{0.05423m})[/tex]Solving the operations:
[tex]W=3.28\times10^{-5}J[/tex]This is equivalent to:
[tex]W=32.8\mu J[/tex]Therefore, the work required is 32.8 micro joules.
