1. Faraday's Law: A circular loop of wire of radius a and resistance H is placed in a time...

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1. Faraday's Law: A circular loop of wire of radius a and resistance H is placed in a time varying
magnetic field B = ti.-,,Boe't that is normal to the plane of the loop. Show that the power dissipated in the loop in the form of Joule's heat (P = L2 = PR} is: oia2Boa)2e-.2crt
P — 2. Maxwell's equations. Assume an electromagnetic wave exists in space with its electric field given by:
E (x, z) = rozcos (cot - kzz) + Eoxcosa.ot — kxx) a) What should the constants Ect and Ecb, be such that all Maxwell's equations in a source free region are satisfied? Hint : Gauss's law has to be satisfied in this region. b) Once you find the restriction for Eoz and Eox find the corresponding H-field using Maxwell's 2nd curl equation. Notice that since the E-field and H-field are coupled together by both curl equations, there is only one H-field that corresponds to this E-field.

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Robert · Accepted Answer

1. Faraday’s Law: A circular loop of wire of radius a and resistance R is placed in a time-
varying magnetic field 0ˆ
t
nB e
B a  that is normal to the plane of the loop. We wish to 
show that the power dissipated in the loop in the form of Joule heat  2 2/P V R I R   is 
given by
 
2
2 2
0
.
ta B e
P
R
  

According to Faraday’s law, the magnitude V of the EMF induced in the wire, due to the 
changing magnetic flux inside it, is given by
 ,B
d
V
dt


where B  is the magnetic flux within the loop. Now we have
 ˆ ,B n
S
dA  B a
where the integral is over the interior S of the loop. Thus we have
 
 
0
0
0
0
2
0
2
0
ˆ ˆ
ˆ ˆ
( )
.

1. Faraday's Law: A circular loop of wire of radius a and resistance H is placed in a time varying magnetic field B = ti.-,,Boe't that is normal to the plane of the loop. Show that the power...

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