How Fast Must a Magnetic Field Change to Induce a Specific Current?

In summary, the conversation discusses a problem involving a single conducting loop of wire with a given area and resistance, and a perpendicular magnetic field of known strength. The goal is to determine the necessary rate of change in the magnetic field to induce a specified current in the loop. Relevant equations are mentioned and the steps to solve the problem are outlined.
  • #1
triplezero24
16
0
Ok, I need a lot of help on this one. A single conducting loop of wire has an area of 7.4*10^-2 m^2 and a resistance of 110 ohms. Perpendicular to the plane of the loop is a magnetic field of strength 0.18 T. At what rate (in T/s) must this field change if the induced current in the loop is to be 0.22 A?

So far all I can figure out is that Phi=BA. And I don't think that has anything to do with this problem. :grumpy:

Thanks for any and all help.
 
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  • #2
Well, how do you relate the change in flux to the induced EMF? And once you have that, just use ohm's law to get the current.
 
  • #3
you should know these formulae from your text

flux [tex] \Phi = \int B dA Cos \theta[/tex]
and induced emf [tex] E = \frac{d \Phi}{dt} [/tex]
and also the induced Emf is just live a voltage really so E = IR.

now try and rearrange these equatios to solve
 

What is Faraday's law of induction?

Faraday's law of induction states that when a conductor is moved through a magnetic field or when there is a change in the magnetic field through a conductor, an electromotive force (EMF) is induced in the conductor. This phenomenon is the basis for generators and many other electrical devices.

What is the mathematical representation of Faraday's law of induction?

Faraday's law of induction can be mathematically represented by the equation EMF = -N(dΦ/dt), where EMF is the electromotive force induced in the conductor, N is the number of turns in the conductor, and dΦ/dt is the rate of change of magnetic flux through the conductor.

How does Faraday's law of induction relate to Lenz's law?

Faraday's law of induction and Lenz's law are closely related. Lenz's law states that the direction of the induced current in a conductor will always oppose the change that caused it. This is a direct consequence of Faraday's law of induction, as the induced current creates its own magnetic field that opposes the change in the original magnetic field.

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

Faraday's law of induction is used in a variety of real-world applications, such as generators, transformers, and induction cooktops. It is also the principle behind electromagnetic induction, which is used in devices like magnetic levitation trains and metal detectors.

How does the strength of the magnetic field and the speed of the conductor affect the induced EMF?

According to Faraday's law of induction, the induced EMF is directly proportional to the rate of change of magnetic flux through the conductor. This means that a stronger magnetic field or a faster-moving conductor will result in a higher induced EMF. However, the number of turns in the conductor also plays a role in determining the induced EMF.

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