MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.02
Radiation from a Light Bulb
A light bulb puts out 100 W of electromagnetic radiation. What is the time-average
intensity of radiation from this light bulb at a distance of one meter from the bulb? What
are the maximum values of electric and magnetic fields, E0 and B0 , at this same distance
from the bulb? For simplicity you may assume that the electromagnetic radiation is in
the form of a plane wave of wavelength ! .
Solution:
The time averaged intensity of radiation on the surface of the sphere of radius r = 1.0 m
is the time averaged power radiated by the light bulb divided by the area of the sphere.
Thus
I =
P
100 W
=
= 8.0 W " m -2
2
4! r
4(3.14)(1.0 m)2
Recall that the time averaged intensity is equal to the magnitude of the time averaged
Poynting vector
! !
E!B
!
.
I = S =
µ0
If we assume a plane wave solution for the electric and magnetic fields then
2
2
!
1 E0 B0 1 E0
1 E0
1
I = S =
=
=
c = ! 0 E0 2 c
2
2 µ0
2 µ0 c 2 µ0 c
2
Therefore the maximum amplitude of the electric field is
Emax = E0 =
2 I
2(8.0 W " m -2 )
=
= 77.4 V " m -1
c! 0
(3.00 # 10 8 m " s-1 )(8.85 # 10 $12 C2 " N -1 " m -2 )
and the maximum amplitude of the magnetic field is
Bmax
E0
78 V ! m -1
= B0 =
=
= 2.6 " 10 #7 T
8
-1
c
3.00 " 10 m ! s