a conducting rod of length `L = 30.0 cm` movies in a magnetic field `vec(B)` of magnitude `0.450 T` directed into the plane of the figure. The rod moves with speed `v = 5.00 m s^(-1)` in the direction shown.

(a) What is motional emf inuced in the rod ?
(b) What is the potential difference between the ends of the rod?
( c) When point, `a or b`, is at higher potential?
(d) When the charges in the rod are in equilibrium, what are the magnitude and direction of the electric field within the rod?
(e) When the charges in the rod are in the rod in equilibrium, which point, `a or b`, has an excess of positive charge?

Explanation

(a) `epsilon = vBL = (5.00m//s)(0.450 T)(0.300m) = 0.675 V`.
(b) The potential difference between the ends of the rod is just the motional emf
( c) The positive charges are moved to end `b`, so `b` is at a higher potential.
(d) `E = (V)/(L) = 0.675 V/(0.300m) = 2.25m^(-1)`.
`b`.