b
Potential gradient along wire \(=\frac{\text { potential difference along wire }}{\text { length of wire }}\)

or, \(0.1 \times 10^{-3}=\frac{1 \times 40}{1000} \,\mathrm{V} / \mathrm{cm}\)

or, Current in wire, \(I\) \(=\frac{1}{400} \,\mathrm{A}\)

or, \(\frac{2}{40+R}=\frac{1}{400}\) or \(R=800-40=760\,\Omega\)