A U-shaped ideal conducting frame and a sliding rod PQ of resistance R, start moving with the velocities v and 2v respectively parallel to a long wire carrying steady current I, as shown in the figure 

 

Charge on the capacitor at time t is $q=\frac{C{\mu }_{0}iv\ln 2}{\pi }(1-e^{-t/RC})$

Current passing through the capacitor at time t is $\frac{{\mu }_{0}iv\ln 2}{\pi R}\left(e^{-t/RC}\right)$

Charge on the capacitor at time t is $q=\frac{C{\mu }_{0}iv\ln 2}{2\pi }(1-e^{-t/RC})$

Current passing through the resistor at time t is $\frac{{\mu }_{0}iv\ln 2}{2\pi R}\left(e^{-t/RC}\right)$