Magnetoelectric induction, I think

[Dante68]

Homework Statement

All I've been given concerning this problem is the diagram below and the instruction to solve for the total voltage at both voltmeters.

Unfortunately, I am not sure whether this configuration counts as a electromagnetic coil, or whether it is simply two single-wire circuits, one for each voltmeter, connected at Points A and B. It also isn't clear from the diagram whether voltmeter #1, and its associated circuit, is in the same plane as the other voltmeter.

The known data:
radius = .1m (A = .01pi)
magnetic flux density = 100w/m^2 or 100 Teslas
frequency = 1000 kHz

Homework Equations

I have been assuming that this each circuit is a coil (with one turn) and that I can use Faraday's Law: EMF = dphi/dt

where phi = the magnetic flux = B*A*cos(theta)

The Attempt at a Solution

Quite frankly, I'm stuck. I'm not sure what 'theta' represents. B*A = 100w/m^2*.01m^2*pi = pi webers, so flux = pi * cos(theta). Is theta the angle of the coil? And once I get phi, how to I use Faraday's Law?

 

[tjkubo]

I am not sure about the diagram, but since they say that the magnetic field is a sine wave, the magnetic field B must vary with time. Write B as a function of time.

 

[nlightner]

Based on the information provided, it seems that this problem involves magnetoelectric induction, which is the process of generating an electric current through the interaction of a magnetic field and an electric field. In this case, the setup appears to be a configuration of two single-wire circuits connected at Points A and B, with each circuit containing a voltmeter. It is unclear from the diagram whether the voltmeters are in the same plane or not.

To solve for the total voltage at both voltmeters, you can use Faraday's Law, which states that the induced electromotive force (EMF) is equal to the rate of change of magnetic flux through a surface. In this case, the magnetic flux is given by B*A*cos(theta), where B is the magnetic flux density, A is the area of the circuit, and theta is the angle between the magnetic field and the normal to the circuit. It is not clear from the given information what value to use for theta, so it would be best to clarify this with the instructor or assume a value for theta (e.g. 0 or 90 degrees) and proceed with the calculation.

Once you have calculated the magnetic flux, you can use Faraday's Law to determine the induced EMF, which will give you the total voltage at both voltmeters. Keep in mind that the frequency of the magnetic field also plays a role in the calculation, so you will need to incorporate that into your solution as well.

If you are still unsure about the approach to take, it may be helpful to consult with your instructor or a colleague for further guidance. It is important to have a clear understanding of the problem and the given information before attempting to solve it.