Typical large values for electric and magnetic fields attained in laboratories a
ID: 1516939 • Letter: T
Question
Typical large values for electric and magnetic fields attained in laboratories are about 1.0 times 10^4 V/m and 2.0T. Determine the energy density for electric field. Express your answer to two significant figures and include the appropriate units. Determine the energy density for magnetic field. Express your answer to two significant figures and include the appropriate units. What magnitude electric field would be needed to produce the same energy density as the 2.0-T magnetic field? Express your answer to two significant figures and include the appropriate units.Explanation / Answer
A) Energy density for electric field,
uE = 0.5*epsilon*E^2
= 0.5*8.854*10^-12*(1*10^4)^2
= 4.43*10^-4 J/m^3
B) magnetic energy density, uB = B^2/(2*mue)
= 2^2/(2*4*pi*10^-7)
= 1.59*10^6 J/m^3
C) Apply, uE = uB
epsilon*E^2/2 = B^2/(2*mue)
E^2 = B^2/(mue*epsilon)
E = B/sqrt(mue*epsilon)
= B*c
= 2*3*10^8
= 6*10^8 V/m
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