In the figure below, the rolling axle, 2.90 m long, is pushed along horizontal r
ID: 1446958 • Letter: I
Question
In the figure below, the rolling axle, 2.90 m long, is pushed along horizontal rails at a constant speed
v = 4.00 m/s.
A resistor
R = 0.4000
is connected to the rails at points aand b, directly opposite each other. The wheels make good electrical contact with the rails, so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R. A uniform magnetic field
B = 0.1100 T
is vertically downward.
(a) Find the induced current I in the resistor.
(b) What horizontal force F is required to keep the axle rolling at constant speed?
Explanation / Answer
R = 0.40
v = 4.00 m/s
B = 0.11 T
(a)
emf generated, e = B*l*v
We know, I = e/R
I = (B*l*v)/R
I = (0.11*2.9*4.0)/0.4
I = 3.19 A
Induced current I in the resistor, I = 3.19 A
(b)
F = B*I*L
F = 0.11 * 3.19 * 2.9 N
F = 1.02 N
F is required to keep the axle rolling at constant speed, F = 1.02 N