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

In summary, the conversation discusses the calculation of the average value of the magnetic field produced by a 15 mW laser with a 2mm diameter beam. The formula E^2 = E^2_0/2 is mentioned, but additional help is needed to set up the problem and solve for it. The Poynting vector is also mentioned, as well as a relationship between Em and Bm that can be found in a book.
  • #1
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 :wink:
 
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  • #2
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: Em and Bm. To eliminate Em, there is a simple relationship between it and Bm, and you should be able to find it in your book without any trouble.
 
  • #3

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.
 

1. What is the formula for calculating average magnetic field for a 15 mW 2mm laser beam?

The formula for calculating average magnetic field for a 15 mW 2mm laser beam is: B = 2μ0P/(πr^2), where B is the magnetic field, μ0 is the permeability of free space, P is the power in watts, and r is the radius of the laser beam in meters.

2. How do you determine the power of a 15 mW 2mm laser beam?

The power of a laser beam is typically given in milliwatts (mW) and can be measured using a power meter. The power meter should be placed perpendicular to the laser beam and the reading recorded. This value can then be used in the formula for calculating average magnetic field.

3. What is the significance of calculating average magnetic field for a laser beam?

Calculating average magnetic field for a laser beam is important for understanding the effects of the magnetic field on the beam's trajectory and intensity. This information can be used to optimize the beam's performance and minimize any potential interference.

4. Are there any safety considerations when working with a 15 mW 2mm laser beam?

Yes, there are safety considerations when working with any laser beam, including a 15 mW 2mm laser beam. It is important to always wear appropriate eye protection and follow proper laser safety protocols. Additionally, any calculations or experiments involving lasers should be conducted in a controlled and supervised environment.

5. Can this formula be applied to other laser beams with different power and radius?

Yes, this formula can be applied to other laser beams with different power and radius. However, it is important to note that the results may vary depending on the specific characteristics of the laser beam being used. It is always best to consult with a knowledgeable scientist or engineer when making calculations for a specific laser beam.

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