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Inductance in a loop of wire

  • Thread starter AStaunton
  • Start date
  • #1
105
1
the problem given is:
A circular loop of wire can be used as a radio antenna. If a 22.0-cm-diameter antenna is located 2.20km away from a 95.0-MHz source with a total power of 55.0kW, what is the maximum emf induced in the loop? (Assume that the plane of the antenna loop is perpendicular to the direction of the radiation's magnetic field and that the source radiates uniformly in all directions.)

As far as I have gotten in solving the problem:
as the loop of wire is at a distance of 2.2km from transmitter we want to find how much energy the loop of wire is getting:

((area of loop of wire)/(surface area of 2.2km sphere))*(power of transmitter)

and plugging numbers in (in mks units) gives:

((.11^2*pi)/(2200^2*pi)*55000) = 3.43*10^-5W

I would be very grateful for a nudge in the right direction...I'm fairly sure there must be a convenient equation derived from laws of inductance that links the power going through the loop, the Frequency (95Mhz) and the induced Voltage which is the variable I want to find.

Thanks

Andrew
 

Answers and Replies

  • #2
105
1
it occurs that maybe the relevant equation here is simply:

P = VI

where as I already stated P for the loop = 3.43*10^-5W

still can't figure what should be done from here...

Still not positive that P = VI is that right eqtion to use!!
 
  • #3
105
1
futher update:

forget that P = VI crap!!

it seems that this problem involves Faraday's law:

EMF= d(phi)/dt

so as loop as perpendicular to propogation, phi is simply B*A.

A=.11^2*3.14 ---> as per the values given in the problem..

to find B:

we know intensity, I:

55000/(22000^2*4*3.14) = 9.05*10^-4 W/m^2

also we know I = EmaxBmax/2(mu_0)

so can find Bmax from this:
=> Bmax = 2.76(10^-9)

so (phi) = Bmax*A=1.048(10^-10)

so to find d(phi)/dt is it simply a matter of dividing the above value by the frequency that was told in the question (95MHz)?

But this apparantly is not the correct answer.....

Be very grateful if someone could inform me of whatever mistakes I am making...cheers
 

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