In the figure below, a metal rod is forced to move with constant velocity along
ID: 2060204 • Letter: I
Question
In the figure below, a metal rod is forced to move with constant velocity along two parallel metal rails, connected with a strip of metal at one end. A magnetic field = 0.340 T points out of the page.(a) If the rails are separated by 29.0 cm and the speed of the rod is 58.0 cm/s, what emf is generated?
(b) If the rod has a resistance of 20.0 and the rails and connector have negligible resistance, what is the current in the rod? (Include the sign, taking counterclockwise to be positive.)
(c) At what rate is energy being transferred to thermal energy?
Explanation / Answer
(a) The emf is the rate of change in the flux through the loop, which would be the magnetic field times the rate of change opf area, or l*v*B = .29*.58*.340 = .0572 V.
(b) Since there is no picture, I'm not sure which direction the rod is moving, but the current would be .0572/20 = 2.86 x 10^-3 A (assuming those are ohms, there are no units in the question). Since the flux is decreasing, the d/dt points into the page, and so, to oppose this change (Lenz's Law), the current flows counterclockwise.
(c) The rate of energy tranfer is the heat dissipated in the rod, V^2/R = (.0572)^2/(20)= 1.64 x 10^-4 J/s(again, assuming those are ohms, if they are milliohms, multiply this, and the current, by 10^3)