What Is the Induced EMF in a Moving Conductor?

[resvordog]

A metal wire slides on a horseshoe-shaped metal loop of width 0.25 m. The loop has negligible resistance, but there is a 1Ω resistor in the circuit as well as a 6 volt battery. There is a uniform magnetic field directed into the plane of the page of magnitude 0.5 T. The slide wire is pushed to the right by the magnetic force. A force of 0.25 N to the left is required to keep it moving a constant speed to the right, i.e. 0.25 N balances the magnetic force.

(a) What is the current in the circuit?
(b) What is the voltage drop across the resistor?
(c) What is the induced emf generated by the moving wire?
(d) With what speed is the wire moving?
(e) What mechanical power (i.e., Fv) does the motor produce?
(f) Subtract from the total electrical power input, the power dissipated in the resistor and compare to the mechanical power.



Relevant equations
F=IlB F=((B^2)(l^2)/R) x v V=IR emf=Blv P=Fv P(dissapated)=(I^2)R


The attempt at a solution
(a) 0.25=I(0.25m)(0.5T) I=2amps
(b) V=(2A)(1Ω) V= 2 volts
(c) 0.25N=((0.5^2)(0.25^2)/(1Ω)) x v
v=16m/s emf=Blv=(0.5T)(0.25m)(16m/s)= 2 volts
(d) v=16m/s
(e) P=(0.25N)(16m/s)= 4 watts
(f) total power input = VI= 2volts x 2 amps = 4 watts
4 watts - 4 watts = 0 watts
0 watts ≠ 4 watts

No idea if I did this right. Please help me! Thanks in advanced.

 

[resvordog]

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