Question

How much work is required to bring a 10 μC charge from infinity to 5.00 meters away from a point charge of -2 μC?

Answer 1

The work done to move one charge from infinity to a given distance is:

$W=q(V_b-V_a)$

since

$V_b-V_a=kQ(\frac{1}{r_b}-\frac{1}{r_a})$

and

$r_a=\infty\rightarrow\frac{1}{r_a}=0$

Then

$W=\frac{kqQ}{r_b}$

where:

$\begin{gathered} k=9\cdot10^9Nm^2C^{-2}\rightarrow eletric\text{ constant} \\ q=-2\mu C=-2\cdot10^{-6}C \\ Q=10\mu C=10\cdot10^{-6}C \\ r_b=5.00m \end{gathered}$

Plug all the data in the formula above:

$\begin{gathered} W=\frac{(9\cdot10^9)\cdot(-2\cdot10^{-6})\cdot(10\cdot10^{-6})}{(5.00)} \\ W=-36\cdot10^{-3} \\ W=-3.6\cdot10^{-4}J \end{gathered}$

So the final answer is:

$W=-3.6\cdot10^{-4}J$