Circuit/Magnetic Field: Find EMF Induced

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In summary, a bar of length 22 cm that slides on two rails is connected to make a complete electrical circuit. A magnetic field of strength 0.05 T exists in the space where the bar is located. The distance between the rails is 20 cm and the initial sliding velocity of the bar is 12 cm/s. Using the universal flux rule, the magnitude of the induced emf can be calculated as Bvl, where B is the magnetic field strength, v is the sliding velocity, and l is the length of the rails.
  • #1
bsmack
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Homework Statement



A bar of length 22 cm that slides on two rails are connected together to make a complete electrical circuit. A magnetic field of strength 0.05 T directed out of the paper exists throughout the regions of space in which this machine is located. Assume that the distance between the rails l=20 cm and that initiaully the bar's sliding velocity is v=12 cm/s. Find the magnitude of the emf induced in this circuit.

Homework Equations



What equations should I be looking at? If it's an equation involving an integral, please give the final equation and possibly an explanation.

The Attempt at a Solution



The only equation I have available to me is emf = integ(E * dl). I don't know how I would get the electric field with the variables given, and I also don't know how I would get dl, as I don't think the length of the rails is given, just the length of the bar going across the rails and the distance between the rails.
 
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  • #2
use the universal flux rule.

emf = d(phi)/dt = B da/dt = Bl dx/dt = B v
 
  • #3
So, my answer should be B*v=0.006 V? This is from a practice final, and the answer listed is 0.0012 V. Did we forget to multiply by 2 somewhere?
 
  • #4
Check your units, bsmack. Does B v have the units of time derivative of flux? You see there is a slight typo in estel's final line. It should read [tex] B L v [/tex]. What is the value of L for your system? (Make sure you pick the right one!)
 
Last edited:
  • #5
I think I figured it out. It should be emf = Bvl, correct?
 
  • #6
Yes, you have it now. Just figure out what L is.
 

FAQ: Circuit/Magnetic Field: Find EMF Induced

1. What is an EMF (electromotive force) induced in a circuit?

An EMF is an electric potential difference created within a circuit due to a changing magnetic field. It is responsible for driving electrical current through a conductor.

2. How is EMF induced in a circuit?

EMF can be induced in a circuit through two methods: electromagnetic induction and Faraday's law. Electromagnetic induction occurs when a conductor moves through a magnetic field, creating a current. Faraday's law states that an EMF is induced in a circuit when the magnetic flux through a loop of wire changes over time.

3. What factors affect the magnitude of the induced EMF?

The magnitude of the induced EMF depends on several factors, including the strength of the magnetic field, the speed of the movement of the conductor, and the angle between the magnetic field and the conductor.

4. How is EMF induced in a generator?

A generator works by rotating a coil of wire within a magnetic field. As the coil rotates, the magnetic field passing through it changes, inducing an EMF in the wire. This EMF then drives the flow of electrons and creates an electric current.

5. Is EMF induced in all types of circuits?

No, EMF is only induced in circuits that have a changing magnetic field. Constant magnetic fields do not induce EMF, so circuits that are not moving or have a constant current will not experience induced EMF.

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