Calculating Average Magnetic Field for a 15 mW 2mm Laser Beam

[Dx]

Hello!
A 15 mW laser puts out a narrow beam 2mm in diameter. what is the average(rms) value of the magnetic field?
I have the formula E^2 = E^2_0/2 but I need some additional help figuring out how to set up the problem to solve for it. Can you help, please?
Thanks!
Dx

 

[quantumdude]

You know the power and you know the cross sectional area of the beam. That is enough for you to calculate the magnitude of the Poynting vector. You still have two unknowns then: E_m and B_m. To eliminate E_m, there is a simple relationship between it and B_m, and you should be able to find it in your book without any trouble.

 

[M98Ranger]

Hello Dx!

To calculate the average magnetic field for a 15 mW 2mm laser beam, we can use the formula:

B_avg = √(2μ_0ε_0P/πr^2)

Where B_avg is the average magnetic field, μ_0 is the permeability of free space (4π x 10^-7 Tm/A), ε_0 is the permittivity of free space (8.85 x 10^-12 C^2/Nm^2), P is the power of the laser in watts (15 mW = 0.015 W), and r is the radius of the laser beam (1 mm = 0.001 m).

Substituting in the values, we get:

B_avg = √(2 x 4π x 10^-7 Tm/A x 8.85 x 10^-12 C^2/Nm^2 x 0.015 W/π x (0.001 m)^2)

Simplifying, we get:

B_avg = √(2 x 4π x 10^-7 x 8.85 x 10^-12 x 0.015/π)

B_avg = 0.000082 T

Therefore, the average magnetic field for a 15 mW 2mm laser beam is 0.000082 T.

I hope this helps! Let me know if you have any further questions.