Induced EMF in a Pair of Circular Wires with Changing Magnetic Field

In summary, two circular wires with radii b and 2b are located on the same plane and share the same center. The smaller wire has a magnetic field of strength B coming out of the paper towards the observer, covering a circular area with radius A. The field is changing at a constant rate, resulting in an induced emf of e in the smaller wire. The question asks for the induced emf in the larger wire, which should be the same as the smaller wire due to the area of the field being contained within the circumference of both wires. Biot-Savart's equation can be used to find the field as a function of radius and work towards the answer.
  • #1
adaschau2
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Homework Statement


The setup is a pair of two circular wires, a small one of radius b and a large one with radius 2b, both sharing the same center and located on the same plane. There is a magnetic field of strength B within the smaller circle that comes out of the paper towards the observer. The field covers a circular area with radius A such that A<b. The magnetic field is changing at a constant rate and creates an induced emf of e in the smaller wire. What is the induced emf in the larger wire?

Homework Equations


e=-delta(flux)/delta(t)
magnetic flux=B*A*cos theta
theta=0 degrees

The Attempt at a Solution


As far as I can tell, the induced emf should be the same for both wires because the area of the field is contained within the circumference of both wires, so each has the same change in magnetic flux over time. The only other way I would think possible is if the distance away from the wire has an affect in the induced emf, but I can't think of any equations that deal with the distance between the magnetic field and the wire. You're input is most appreciated!
 
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  • #2
Biot-Savart is your equation of choice here, try find the field as a function of radius and work on the answer from there...
 

1. What is induced emf?

Induced emf, or electromotive force, is the voltage generated in a circuit due to changes in the magnetic flux through the circuit. It is a result of Faraday's Law of Induction, which states that a changing magnetic field will induce an electric field.

2. How is induced emf related to magnetic flux?

Induced emf is directly proportional to the rate of change of magnetic flux through a circuit. This means that the greater the change in magnetic flux, the greater the induced emf will be.

3. Can induced emf be positive or negative?

Yes, induced emf can be positive or negative depending on the direction of the change in magnetic flux. If the change in flux is in the same direction as the current flow, the induced emf will be positive. If the change in flux is in the opposite direction, the induced emf will be negative.

4. What factors affect the magnitude of induced emf?

The magnitude of induced emf is affected by the strength of the magnetic field, the rate of change of the magnetic flux, and the number of turns in the circuit. Increasing any of these factors will result in a greater induced emf.

5. How is induced emf used in practical applications?

Induced emf is used in various devices, such as generators and transformers, to convert mechanical energy into electrical energy. It is also used in induction cooktops, which use induced emf to heat up metal pots and pans. Additionally, induced emf is used in electromagnetic braking systems, where it creates a magnetic field that slows down moving objects.

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