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Inductance caused by radio antenna

by squib
Tags: antenna, caused, inductance, radio
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squib
#1
Feb23-06, 12:42 AM
P: 40
A circular loop of wire can be used as a radio antenna. If an antenna with a diameter of .215 m is located a distance of 2.50 km away from a from a source with a total power of 57.0 kW at a frequency of 102 MHZ, 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.)

I figure that B(t) = (Bmax)sin(wt)
Magnetic moment = A*(Bmax)sin(wt)
E=d[A*(Bmax)sin(wt)]/dt = AB_max(cos(wt))w
since I'm looking for max, i set cos(wt) to 1, therefore
E=A(B_max)w = A(B_max)(2pi(frequency))

A=pi(.1075)^2
I=(57*10^3)/((4/3)pi(2.5*10^3)^3))
B_max=sqrt([2I(u_0)]/c)
E=B*A*2*pi*f <--- this does not work however

I am wondering where I went wrong....
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