How large an emf (rms) will be generated in an antenna that consists of a 426 lo
ID: 1895807 • Letter: H
Question
How large an emf (rms) will be generated in an antenna that consists of a 426 loop circular coil of wire 1.54 cm in diameter if the EM wave has a frequency of 886 kHz and is transporting energy at an average rate of 1.17E-4 W/m2 at the antenna?Attempt at solution:
N*B*A*w*sin(w*t) = N*A*w*rt(u*S/c)
= N*A*2*pi*wave*rt(u*S/c)
N = 426
A = pi*.0154^2
=7.4506011372535536443380050477857e-4
w = 2*pi*886000
=5566902.1821611136185558040751713
u = 4*pi*10^-7
=1.2566370614359172953850573533118e-6
S = 1.174*10^-4
0.0001174
c = 3*10^8
299792458
1766910.3052719663978891793767263*7.0150154037910343671130568089972e-10
= 0.00123949030085999631603673679581 V
Explanation / Answer
Erms = N*A*w*Brms = N*A*w*sqrt(U0*S/c) = 426 * Pi*(1.54*10^-2)^2*2Pi*8.86*10^5*sqrt[(4Pi*10^-7*1.17*10^-4)/(3*10^8)] = 12.35 x 10^-4 V
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