Magnet through Loop (Faraday's Law?)

In summary, the conversation discusses the use of Faraday's Law to calculate the average emf induced in a rectangular loop when a constant magnetic field is passing through it. Part (a) asks for the magnitude of the emf when the magnetic field decreases to zero in 0.40 seconds, while part (b) asks for the rate at which the area of the loop should change to maintain the same magnitude of emf. The conversation also addresses a discrepancy in the numbers used in the calculation.
  • #1
Magnet through Loop (Faraday's Law??)

A constant magnetic field passes through a single rectangular loop whose dimensions are 0.35 m 0.55 m. The magnetic field has a magnitude of 2.1 T and is inclined at an angle of 50° with respect to the normal to the plane of the loop.
(a) If the magnetic field decreases to zero in a time of 0.40 s, what is the magnitude of the average emf induced in the loop?
(b) If the magnetic field remains constant at its initial value of 2.1 T, what is the magnitude of the rate A / t at which the area should change so that the average emf has the same magnitude as in part (a)?

I used Faraday's Law: emf=-N(change in flux/change in time)

For part (a), I used Faraday's law and plugged in magnetic flux=BAcos50 for the change in flux. The Area and the cosine is the same, so the equation reduced down to emf=-N*A*cos50*(B final-B initial/time).

For area I multiplied the length and width of the rectangular loop. So when I plugged in the numbers into the equation I got emf=-1*0.1925*cos50*(0-2.1/40) and I got the emf to be 0.00649617 Volts. Apparently this wasn't the correct answer when I plugged it in. Am I doing something wrong??

For part (b) I can't get until I get part (a) first. Could you please help me and tell me if I did something wrong. Thanks a lot!
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  • #2
firstly, in your question you said 0.40s later you used 40 in your equation... which is correct?
  • #3
Yeah your right, sorry about that, guess I read it wrong. That was really stupid of me. Thanks for your help!

What is Faraday's Law?

Faraday's Law, also known as the law of electromagnetic induction, states that a changing magnetic field can induce an electric current in a conductor.

How does a magnet passing through a loop demonstrate Faraday's Law?

When a magnet moves through a loop of wire, it creates a changing magnetic field, which in turn induces an electric current in the wire according to Faraday's Law.

What factors affect the amount of current induced in the loop?

The amount of current induced in the loop depends on the strength and speed of the magnet, the number of loops in the wire, and the resistance of the wire.

Is the direction of the induced current determined by the direction of the magnet's movement?

Yes, according to Lenz's Law, the direction of the induced current will oppose the change in the magnetic field caused by the magnet's movement. This means that the direction of the current will depend on the direction in which the magnet is moving.

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

Faraday's Law has many practical applications, including generators, transformers, and induction cooktops. It is also the basis for many modern technologies, such as electric motors and power plants.

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