Induced Electric Field and Faraday's law

In summary: BMax = 30.9 TBMin = 29.6 TdB/dt = 19.5 T/sIn summary, the Francis Bitter National Magnet Laboratory at M.I.T. operates a 3.3 cm diameter cylindrical magnet producing a 30 T field. The field's magnitude can be varied sinusoidally between 29.6 T and 30.9 T at a frequency of 15 Hz. Using Faraday's law, the maximum value of the induced electric field at a radial distance of 1.6 cm from the axis can be calculated by setting up an equation and differentiating it with respect to time, taking into account the factor of
  • #1
DarkWarrior
5
0
Hello, I'm stuck (again) on a physics problem.

The problem:

Early in 1981 the Francis Bitter National Magnet Laboratory at M.I.T. commenced operation of a 3.3 cm diameter cylindrical magnet, which produces a 30 T field, then the world's largest steady-state field. The field magnitude can be varied sinusoidally between the limits of 29.6 and 30.9 T at a frequency of 15 Hz. When this is done, what is the maximum value of the magnitude of the induced electric field at a radial distance of 1.6 cm from the axis?

What I've done so far: I've used Faraday's law, and after messing around with the equation I got E = (r/2)(dB/dt). As I understand it, the induced electric field is inside the magnetic field (r is less than R), so I thought this equation was correct.

R= .0165 m
r = .016 m
dB/dt = 19.5 Tesla/second. Since the frequency is 15, you multiply the difference of 30.9 and 29.6 by 15, getting 19.5

However when I plug the numbers in, my answer comes out wrong. Can someone point out where I screwed up? Thank you!
 
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  • #2
DarkWarrior said:
Hello, I'm stuck (again) on a physics problem.

The problem:

Early in 1981 the Francis Bitter National Magnet Laboratory at M.I.T. commenced operation of a 3.3 cm diameter cylindrical magnet, which produces a 30 T field, then the world's largest steady-state field. The field magnitude can be varied sinusoidally between the limits of 29.6 and 30.9 T at a frequency of 15 Hz. When this is done, what is the maximum value of the magnitude of the induced electric field at a radial distance of 1.6 cm from the axis?

What I've done so far: I've used Faraday's law, and after messing around with the equation I got E = (r/2)(dB/dt). As I understand it, the induced electric field is inside the magnetic field (r is less than R), so I thought this equation was correct.

R= .0165 m
r = .016 m
dB/dt = 19.5 Tesla/second. Since the frequency is 15, you multiply the difference of 30.9 and 29.6 by 15, getting 19.5

However when I plug the numbers in, my answer comes out wrong. Can someone point out where I screwed up? Thank you!
Set up the equation for the field as a function of time (B = sinusoidal term + constant). Then differentiate with respect to time. There will be a factor [itex]\omega = 2\pi/T[/itex] in the equation.

AM
 
  • #3


Hello there,

It looks like you have the right idea using Faraday's law to solve this problem. However, there are a few things you need to take into consideration when plugging in the numbers.

First, make sure you are using the correct units for all of your values. The units for dB/dt should be in tesla/second, not just tesla. Also, the units for r and R should be in meters, not centimeters.

Secondly, when calculating the maximum value of the induced electric field, you need to use the maximum value of the changing magnetic field, which in this case is 30.9 T. So your equation should be E = (r/2)(d(30.9)/dt).

Lastly, make sure you convert your frequency from Hz to radians/second before plugging it into the equation. So your final equation should be E = (r/2)(30.9*2π*15) = 14.7πr T.

I hope this helps you solve the problem. Remember to always double check your units and make sure you are using the correct values for each variable. Good luck!
 

1. What is an induced electric field?

An induced electric field is a type of electric field that is created by a changing magnetic field. It is also known as a non-conservative electric field because it does not have a potential function. This type of electric field can be found in electromagnetic induction and is responsible for generating electric currents.

2. How is Faraday's law related to induced electric fields?

Faraday's law states that the induced electromotive force (EMF) in a closed loop is equal to the negative of the time rate of change of the magnetic flux through the loop. In simpler terms, it means that a changing magnetic field will induce an electric field. This is the basis of electromagnetic induction and explains the relationship between induced electric fields and Faraday's law.

3. What factors affect the strength of an induced electric field?

The strength of an induced electric field depends on several factors, including the rate of change of the magnetic field, the number of turns in a coil, and the permeability and area of the material through which the magnetic field is changing. Generally, a faster rate of change and more turns in a coil will result in a stronger induced electric field. Higher permeability and larger surface area also contribute to a stronger induced electric field.

4. How is Lenz's law related to induced electric fields?

Lenz's law is a consequence of Faraday's law and states that the direction of an induced current is always such that it opposes the change that produced it. This means that when a changing magnetic field induces an electric field, the resulting current will flow in a direction that creates a magnetic field that opposes the change in the original magnetic field. This law is important in understanding the behavior of induced electric fields.

5. What are some common applications of induced electric fields and Faraday's law?

Induced electric fields and Faraday's law have many practical applications, including generators, transformers, electric motors, and wireless charging. They are also used in induction cooktops, metal detectors, and magnetic levitation trains. Understanding these principles is essential in the development of many modern technologies.

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