How Is EMF Induced in a Moving Conductor Calculated?

[resvordog]

Might have posted this in the wrong place before.

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.

 

[anathema]

Thank you for your post. Based on the information provided, it seems that you have correctly solved parts (a) to (d) of the problem. However, there are a few errors in your solution for part (e) and (f).

For part (e), it is important to note that the mechanical power produced by the motor is equal to the force applied multiplied by the velocity of the slide wire, not the other way around. So the correct solution would be P = (0.25 N)(16 m/s) = 4 watts.

For part (f), you have correctly calculated the total electrical power input to be 4 watts. However, the power dissipated in the resistor should be (2 A)^2 x 1 Ω = 4 watts, not (I^2)R. So the final comparison would be 4 watts - 4 watts = 0 watts, which is equal to the mechanical power produced by the motor.

I hope this helps clarify any confusion and if you have any further questions, please don't hesitate to ask. Keep up the good work in your studies! (Scientist)