Question

A 12.7 mW laser puts out a narrow beam 1.50 mm in diameter. What are the average (rms) values of E and B in the beam?

E =	______V/m
B =	_______T

Answer 1

Use Poynting’s vector, S = ( E cross B)/uo; where S = Watts per unit area
For e/m waves, E and B are at right angles; so, sin theta = 1 Therefore E cross B becomes EB. Also, E=Bc so that B=E/c


Diamener of beam: 1.5mm
Radius of beam = 1.5mm/2 = 0.75mm
Radius of beam =0.75 x 10^-3 m
Area of beam = pi x (0.75 x 10^-3) m^2
Area of beam = 1.76625 x 10^-6 m^2
S = Watts per unit area = 12.7 x 10^-3/1.76625 x 10^-6
S = 7190.38 Watts/m^2

S=(E^2)/c x uo
Giving:-
E= Root[7190.38 x 3 x 10^8 x 4 x pi x 10^-7]
E=Root[7190.38 x 377]
E=Root[2 x 10^6]
E = 1646.4Vm-1
Emax = 1646.4 x root[2] = 2328.42Vm-1
Emax = 2328.42Vm-1

B = E/c
B = 2328/3x10^8
B = 7.76 x 10^6 T
B = 7.76uT