A point charge of \(10^{-8} C\) is placed at origin. The work done in moving a point charge \(2 \mu C\) from point \(A (4,4,2) m\) to \(B (2,2,1) m\) is _________ J.

Work done by external agent :
\(W _{ ext }=\Delta U ;\)
\(\Delta U \rightarrow\) Change in potential energy in taking the charge from initial to final configuration
\(\Rightarrow W _{ ext }=\frac{1}{4 \pi \epsilon_0} \frac{ q _1 q _2}{ r _{ f }}-\frac{1}{4 \pi \epsilon_0} \frac{ q _1 q _2}{ r _{ i }}\)
Now, \(r_f=\sqrt{(2-0)^2+(2-0)^2+(1-0)^2}=3 m\)
\(r_i=\sqrt{(4-0)^2+(4-0)^2+(2-0)^2}=6 m\)
\(\therefore \quad W _{\text {ext }}=\left(9 \times 10^9\right) \times\left(10^{-8} \times 2 \times 10^{-6}\right)\left[\frac{1}{3}-\frac{1}{6}\right]\)
\(=3 \times 10^{-5}\)
\(=30 \times 10^{-6} J\)