a
(a) Induced current in the circuit \(i = \frac{{Bvl}}{R}\)

Magnetic force acting on the wire \({F_m} = Bil = B\left( {\frac{{Bvl}}{R}} \right)\;l\)

\( \Rightarrow {F_m} = \frac{{{B^2}v{l^2}}}{R}\) External force needed to move the rod with constant velocity

\(({F_m}) = \frac{{{B^2}v{l^2}}}{R} = \frac{{{{(0.15)}^2} \times (2) \times {{(0.5)}^2}}}{3}\)\( = 3.75 \times {10^{ - 3}}N\)