(a) [tex]72.3 W/m^2[/tex]
First of all, we need to find the area of the circular spot, which is given by:
[tex]A=\pi r^2[/tex]
where r is the radius of the spot, which is half the diameter, therefore
[tex]r=\frac{d}{2}=\frac{2.10 mm}{2}=1.05 mm=1.05\cdot 10^{-3} m[/tex]
So, the area of the spot is
[tex]A=\pi (1.05\cdot 10^{-3}m)^2=3.46\cdot 10^{-6} m^2[/tex]
We know that the power output of the laser is
[tex]P=0.250 mW=2.5\cdot 10^{-4} W[/tex]
So the intensity of the laser beam is
[tex]I=\frac{P}{A}=\frac{2.5\cdot 10^{-4} W}{3.46\cdot 10^{-6} m^2}=72.3 W/m^2[/tex]
(b) [tex]7.8\cdot 10^{-7}T[/tex]
The average intensity of the laser is related to the peak magnetic field strength by
[tex]I=\frac{cB_0^2}{2\mu_0}[/tex]
where
c is the speed of light
[tex]B_0[/tex] is the peak magnetic field strength
[tex]\mu_0=1.257\cdot 10^{-6} H/m[/tex] is the vacuum magnetic permeability
Solving the formula for [tex]B_0[/tex], we find
[tex]B_0 = \sqrt{\frac{2I\mu_0}{c}}=\sqrt{\frac{2(72.3 W/m^2)(1.257\cdot 10^{-6} H/m)}{3\cdot 10^8 m/s}}=7.8\cdot 10^{-7}T[/tex]
(c) 234 V/m
The relationship between magnetic field and electric field in an electromagnetic wave is
[tex]E_0=cB_0[/tex]
where
[tex]E_0[/tex] is the peak electric field strength
c is the speed of light
[tex]B_0[/tex] is the peak magnetic field strength
Substituting numbers into the formula, we find
[tex]E_0=(3\cdot 10^8 m/s)(7.8\cdot 10^{-7} T)=234 V/m[/tex]
