A metal rod of resistance $20 \mathrm{\Omega }$ is fixed along a diameter of a conducting ring of radius 0.1 m and lies in an x-y plane. There is a magnetic field $\overrightarrow{B}=(50 \mathrm{T})\widehat{k}.$ The ring rotates with an angular velocity $\omega =20 \mathrm{rad}/\mathrm{s}$ about its axis. An external resistance of $10 \mathrm{\Omega }$ is connected across
the centre of the ring and rim. The current through external resistance is

• A

  $\frac{1}{4}\mathrm{A}$

• B

  $\frac{1}{2}\mathrm{A}$

• C

  $\frac{1}{3}\mathrm{A}$

• D

  zero