Calculating EMF from a Rotating Coil: Max & Avg Values

[danago]

On a particular dynamo, the rotating coil has 500 loops, each of area 2.5x10^-4 m². The magnetic field can assumed to uniform and of magnitude 0.400T. When the bicycle is ridden at a particular speed, the coil rotates with a frequency of 8Hz. What is the maximum emf produced? What is the average emf produced?

Ok. According to lenz's law, the emf is equal to the time rate of change of magnetic flux.

$$\left| \varepsilon \right| = \frac{{d\Phi }}{{dt}} = \frac{d}{{dt}}(NAB\sin \theta ) = \frac{{d\theta }}{{dt}}NAB\cos \theta$$

I am told that it rotates 8 times per second, which is means that the angular frequency is given by:

$$\frac{{d\theta }}{{dt}} = 16\pi$$

Therefore, the EMF is given by:
$$\left| \varepsilon \right| = 0.8\pi \cos \theta$$

The maximum value of $$cos\theta$$ is 1, therefore the maximum EMF is ~2.51V. Is that correct? Also, how should i go about finding the average? Just divide it by $$\sqrt{2}$$?

Thanks in advance,
Dan.

 

[learningphysics]

Looks right to me. yup divide the peak by sqrt(2).

 

[danago]

Ah alright. Thanks for the quick reply