b
Charge located at the origin, \(q=8 \,mC =8 \times 10^{-3} \,C\)

Magnitude of a small charge, which is taken from a point \(P\) to point \(R\) to point \(Q, \;\;q_{1}=-2 \times 10^{-9} \,C\)

All the points are represented in the given figure.

Point \(P\) is at a distance, \(d_{1}=3 \,cm ,\) from the origin along \(z\) -axis. Point \(Q\) is at a distance, \(d _{2}=4 \,cm ,\) from the origin along \(y\) -axis.

Potential at point \(P, \quad V_{1}=\frac{q}{4 \pi \epsilon_{0} \times d_{1}}\)

Potential at point \(Q\), \(\quad V_{2}=\frac{q}{4 \pi \epsilon_{0} d_{2}}\)

Work done \((W)\) by the electrostatic force is independent of the path. \(\therefore W=q_{1}\left[V_{2}-V_{1}\right]\)

\(=q_{1}\left[\frac{q}{4 \pi \epsilon_{0} d_{2}}-\frac{q}{4 \pi \epsilon_{0} d_{1}}\right]\)

\(=\frac{q q_{1}}{4 \pi \epsilon_{0}}\left[\frac{1}{d_{2}}-\frac{1}{d_{1}}\right]\)

Where, \(\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \,N\, m ^{2} \,C ^{-2}\)

\(\therefore W=9 \times 10^{9} \times 8 \times 10^{-3} \times\left(-2 \times 10^{-9}\right)\left[\frac{1}{0.04}-\frac{1}{0.03}\right]\)

\(=-144 \times 10^{-3} \times\left(\frac{-25}{3}\right)\)

\(=1.27 \,J\)

Therefore, work done during the process is \(1.27 \;J\)