Solving for Total Magnetic Flux and Induced EMF

[rock.freak667]

Homework Statement

http://img164.imageshack.us/img164/3313/qqqqo3.jpg

Find the total magnetic flux through the coil at t=0
Given that the rate of change of flux at any time,t, is equal to $2 \pi f \phi sin 2 \pi ft$, find the maximum instanteous value of the induced emf at any time & the rms value of the induced emf.

If the coil were fixed and the magnet rotated at the same rate in the same direction, what difference would this make in the induced emf?

Homework Equations

The Attempt at a Solution

$$\phi = NBA = (150)*(4 \times 10^{-4})*( \pi (\frac{0.1}{2})^2)= 4.7 \times 10^{-4}Wb$$


Max emf at any time.

$$E=2 \pi f \phi sin 2 \pi ft \Rightarrow E_{max}=2 \pi f \phi = 2 \pi (25)(4.7 \times 10^{-4})=0.074V$$

$$E_{RMS}= \frac{0.074}{\sqrt{2}}=0.052V$$

and No change in the emf.


Any part wrong?

 

[dynamicsolo]

If the magnet rotates in the same direction about a fixed coil, then the relative direction of rotation of the coil in the magnetic field is reversed. That won't change the magnitude of the induced emf, but... (I'm not clear as to whether the question is asking only about quantitative differences...)

I concur with your calculations.

 

[Moetasim]

Your solution for finding the total magnetic flux through the coil at t=0 and the maximum instantaneous value of the induced emf at any time is correct. However, your calculation for the RMS value of the induced emf is incorrect. The correct equation for finding the RMS value is E_{RMS}= \frac{E_{max}}{\sqrt{2}}= \frac{0.074}{\sqrt{2}}=0.052V.

As for the last part of the question, if the coil were fixed and the magnet rotated at the same rate in the same direction, the induced emf would still be the same. This is because the flux through the coil is still changing at the same rate and direction, regardless of whether the coil or the magnet is moving. Therefore, the induced emf would not be affected.