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 $R=800-40=760\,\Omega$