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Exploration 29.4: Loop in a Time-Varying Magnetic Field
Please wait for the animation to completely load.
The animation shows a wire loop in a changing magnetic field. The graphs show the magnetic field in the x direction as a function of time and the induced emf in the loop (position is given in meters, magnetic field strength is given in millitesla, 10-3 T, and emf is given in millivolts). Restart.
- The vectors show the field through the loop as a function of time. What do the different colors indicate?
- What impact does changing the maximum value of the magnetic field have on the induced emf?
- What impact does changing the frequency of the oscillation of the magnetic field have?
- Develop an expression to relate the change in the emf to the parameters you can vary.
- Develop an equation for the magnetic field as a function of time and the parameters you can vary.
- What is the area of the loop? Therefore, what is the flux through the loop as a function of time?
- Using Faraday's law, show that the emf should be equal to |Bmax|Aωcos(ωt + φ), where |Bmax| is the maximum value of the magnetic field in the x direction, A is the area of the loop, ω is the angular frequency of the oscillation, and φ is a phase angle.
- Verify that this expression matches the graph for the emf vs. time.
Exploration authored by Anne J. Cox.