Two long, smooth, horizontal metal rails, $0.50\ \text{m}$ apart, lie in a uniform vertical magnetic field of $0.80\ \text{T}$. At one end they are joined by an uncharged capacitor of $0.50\ \text{F}$. A metal rod of mass $0.20\ \text{kg}$ lies across the rails, as in the figure, and is given a push so that it starts sliding away from the capacitor at $7.0\ \text{m/s}$. No other force acts along the rails. The rod and rails together have a resistance of $2.0\ \Omega$. How much heat is produced in the circuit in all, by the time the current has stopped?

Fig. 1: Top view of two long horizontal rails, 0.50 m apart. At their left end a 0.50 F capacitor joins them. A metal rod of mass 0.20 kg lies across the rails at right angles. An arrow shows it sliding to the right, away from the capacitor, at 7.0 m/s. A grid of crosses shows a uniform vertical magnetic field of 0.80 T.