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## Homework Statement

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A radio transmitter radiates isotropically at the frequency of 90.8 MHz. The peak magnetic field at

a receiver, 9km from the transmitter, is ##9x10^{-10}T##. Calculate the maximum amplitude of the induced emf in a 12 turn coil with area A = ##90cm^{2}## at the receiver. Hint: choose the optimal angle.

## Homework Equations

The amplitude of induced emf: ##ε=BAω##

##ε=-N\frac{dΦ}{dt}=-NABωcos(ωt)##

##Φ=NBA##

##Φ=NABsin(ωt)##

##Φ=BAcosθ##

All the equations for Φ are in the lecture slides but how can I know which one is the correct one? Why are there several equations for Φ?

## The Attempt at a Solution

First, I thought I have to find the first derivative etc. to find the absolute maximum since the question is asking about the maximum amplitude. But in one of the lectures we had a similar example (the question was to find the amplitude of the electromotive force induced in the loop by the signal. And the numbers were different, of course). In the example, they used this equation: ##ε=BAω##

If I use the same equation for my problem, I get this:

##ω=(2)(π)(f)##

##ω=(2)(π)(9.08x10^7Hz)=5.7x10^8rad/s##

Plug in:

##ε=BAω##

##ε=(9x10^{-10}T)(0.009m^2)(5.7x10^8rad/s)##

##ε=4.6x10^{-3}V##

However, since the problem includes the hint about the angle, and my solution doesn't include an angle, I'm guessing that my solution is wrong. So how should I approach the problem instead?

Any help is much appreciated!

Many thanks! :)