Solve Faraday's Law: Find Current in Circular Wire

In summary, the drawing shows a copper wire (negligible resistance) bent in a circular shape with a radius of .5 m. The radial section BC is fixed in place, while the copper bar AC sweeps around at an angular speed of 15 rad/s. The bar makes electrical contact with the wire at all times. The wire and bar have negligible resistance. A uniform magnetic field exists everywher, is perpendicular to the plane of the circle, and has a magnitude 3.8E-3T. Find the magnitude of the current induced in the loop ABC.
  • #1
kris24tf
35
0
The drawing shows a copper wire (negligible resistance) bent in a circular shape with a radius of .5 m. The radial section BC is fixed in place, while the copper bar AC sweeps around at an angular speed of 15 rad/s. The bar makes electrical contact with the wire at all times. The wire and bar have negligible resistance. A uniform magnetic field exists everywher, is perpendicular to the plane of the circle, and has a magnitude 3.8E-3T. Find the magnitude of the current induced in the loop ABC.

http://edugen.wiley.com/edugen/courses/crs1000/art/qb/6e/ch22p_26.gif

I thought I had done this right but my answer comes out incorrect. I found the equation E=-NB(deltaA/deltaT) using Faraday's Law. I then went about finding the ratio delta A/ Delta T. I took delta A/pi x r^2 = delta t/delta T. This gave delta A/delta t = pi x r^2/T, which I then got wr^2/2 from, so I found that delta A / delta t = wr^2/2.
However, after plugging the numbers in, my answer was incorrect. I asked my instructor, and he said I was right there with the answer, but I'm not sure where else to go or if I need to use different figures since we're using rad/s for the angular velocity. Any help here at all is appreciated.
 
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  • #2
So what did you get for your answers for the loop voltage (what you call "E") and therefore the current? I get about 7mV and 2.4mA...
 
  • #3
I got the 7.13 mV but I wasn't sure how to get the current from this since it said the resistance was negligible?
 
  • #4
There's an explicit 3 Ohm resistor in series with the wire and wiper. You probably just didn't notice it.
 
  • #5
Oooohhh now I see where the resistance comes from. I was using a number froma different problem somehow. Thanks a lot your answers actually helped me realize what I was doing!
 

What is Faraday's Law?

Faraday's Law is a fundamental principle in physics that describes the relationship between a changing magnetic field and an induced electric field. It states that the induced electromotive force (EMF) in a closed loop is equal to the rate of change of the magnetic flux through the loop.

How do you solve Faraday's Law?

To solve Faraday's Law, you need to know the values of the variables involved: the magnetic flux, the number of turns in the wire, and the time period over which the flux changes. Then, you can use the formula EMF = -N(dΦ/dt) to calculate the induced EMF, and from there, use Ohm's Law (V=IR) to find the current in the circular wire.

What is the significance of a circular wire in Faraday's Law?

A circular wire is often used in Faraday's Law problems because it simplifies the calculation of the magnetic flux. The magnetic flux through a circular loop of radius r is given by Φ = BA, where B is the magnetic field and A is the area of the loop. This makes it easier to calculate the rate of change of the magnetic flux (dΦ/dt) and solve for the induced EMF.

What are some real-world applications of Faraday's Law?

Faraday's Law has many practical applications in our daily lives, including the operation of electric generators and motors, transformers, and induction cooktops. It is also used in technologies such as MRI machines, power plants, and wireless charging.

What are some common misconceptions about Faraday's Law?

One common misconception is that Faraday's Law states that a changing magnetic field produces an electric current. In reality, it is the changing magnetic flux that induces an EMF, which can then cause a current to flow if there is a complete circuit. Another misconception is that Faraday's Law only applies to circular wires, when in fact it can be applied to any shape of conducting loop. Lastly, it is important to note that Faraday's Law only describes the relationship between a changing magnetic field and an induced EMF, not the cause of the change in the magnetic field itself.

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