Faraday Loop Changing Field Model

The EJS Faraday Loop Changing Field models shows the induced emf in a conducting loop in a changing external magnetic field. You can control the frequency, magnitude and type of variation of the external field as you would in a laboratory when using a function generator to produce current in a large wire coil. You can examine and edit the model if Ejs is installed. Information about EJS is available at: <http://www.um.es/fem/Ejs/>.

Questions:

In answering these questions, you may need to adjust the scale of the y-axis (this is like changing your V/div on your oscilloscope in the lab).

1. Run the simulation. Choose a triangle wave for the external field (this means the magnetic field increases linearly with time and then decreases linearly). Describe (or sketch) the output. Explain the induced emf as a function of time (Hint: emf is proportional to dB/dt).

   1. If you double the amplitude of the external field, what happens to the external field? What happens to the induced emf? If you double the frequency what happens to the induced emf? If you double the radius of the loop, what happens to the induced emf? What happens to the induced emf as you change the angle? Why?

   2. What is the slope of the external field as a function of time? How does it compare to the induced emf? How should they be related?

2. Describe the emf waveform for a square wave external magnetic field. Repeat for the sine wave. Explain the shape of the plot you see for the induced emf.

3. For the sine function input, what amplitude do you expect for the induced emf and why? (Hint: This requires taking a derivative.)

4. Assume the external field is generated with current through a large loop and the small loop you see on the screen is in the middle of this much larger loop. The magnetic field at the center of such a loop is given by B=μ₀I/2R. Assume further that you varied the current in that loop to give the varying external field for the small loop you see in the model. By measuring the changing external field (or current in the large loop) and the induced emf, how could you determine the value of μ₀, the permativity of free space?

References:

• Halliday, Resnick and Walker, Fundamentals of Physics, 8th edition, Chapter 29 (2007).

Credits:

The Faraday Loop Changing Field Model was created by Anne J Cox using the Easy Java Simulations (EJS) authoring and modeling tool. 

You can examine and modify a compiled EJS model if you run the program by double clicking on the model's jar file.  Right-click within the running program and select "Open EJS Model" from the pop-up menu to copy the model's XML description into EJS.  You must, of course, have EJS installed on your computer.

Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.