The figure shows a zero-resistance rod sliding to the right on two zero-resistan

Question

The figure shows a zero-resistance rod sliding to the right on two zero-resistance rails separated by the distance L = 0.51 m. The rails are connected by a 11.7-? resistor, and the entire system is in a uniform magnetic field with a magnitude of 0.750 T. (b) What is the rate of energy dissipation in the resistor? mW (c) What is the mechanical power delivered to the rod?

Explanation / Answer

a) force acting on rod = B * i * L E = B*L*v i = E / R = B*L*v / R .125 = .75 * .51 * v / 11.7 ==> v = .125 * 11.7 / (.75 * .51) v = 3.82352941 m/s F = B * i * L = (B*L)^2 * v / R F = (.75 * .51)^2 * 3.82352941 / 11.7 = 0.0478125 N force exerted on rod = 47.8125 mN b) power dissipated = E * i = (B*L*v)^2 / R P = (.75 * .51 *3.82352941)^2 / 11.7 P = 0.1828125 W power dissipated in resistor = 182.8125 mW c) mechanical power delivered = F * v force acting on rod = B * i * L = (B*L)^2 * v / R power delivered = (B*L)^2 * v / R * v P = F *v = 0.0478125 * 3.82352941 = 0.1828125 W mechanical power delivered to the rod = 182.8125 mW the mechanical power delivered is converted into electrical power

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