Electromagnetics Specifically depth problems.

In summary, we can calculate the depth at which the magnetic field is 2.5% of its original value using the equation d = (2/π) * (1/μσω)^0.5 * ln(1/0.025). The electric field on the surface of copper can be calculated using E = cB/μω, with a value of 1.5 V/m in this case. The total power propagated inside the copper can be calculated using P = (1/2) * σ * E^2 * d, with a value of 2.8*10^-7 W. This represents the energy dissipated in the copper due to the incident plane wave.
  • #1
apalmer3
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Homework Statement



A plane wave of 1 MHz frequency in free space is incident normally on a copper
surface [[tex]\sigma[/tex]=5.8*10^7, [tex]\mu[/tex]r=1, and [tex]\epsilon[/tex]r=1]. If the magnetic field strength at the surface is 1 mA m-1, find the depth at
which it is 2.5% of this value. Calculate the value of electric field on the surface
of the copper. Make a comment on the total power propagated inside the copper.


The Attempt at a Solution



I am mostly concerned with how to find the depth at which the magnetic field is 2.5% of its original value. I simply don't have any resources on how to calculate this. Could anybody point me towards the correct equations? Thanks!
 
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  • #2




To calculate the depth at which the magnetic field is 2.5% of its original value, you can use the following equation:

d = (2/π) * (1/μσω)^0.5 * ln(1/0.025)

Where d is the depth, μ is the permeability of the material (in this case, μ = μrμ0 = 1*4π*10^-7), σ is the conductivity of the material (in this case, σ = 5.8*10^7), and ω is the angular frequency (in this case, ω = 2πf = 2π*10^6). This equation is derived from the skin depth formula for conductors.

As for the electric field on the surface of the copper, you can use the following equation:

E = cB/μω

Where E is the electric field, c is the speed of light, B is the magnetic field strength, μ is the permeability, and ω is the angular frequency. In this case, the electric field on the surface of the copper would be 1.5 V/m.

Finally, to comment on the total power propagated inside the copper, we can use the following equation:

P = (1/2) * σ * E^2 * d

Where P is the power, σ is the conductivity, E is the electric field, and d is the depth. Plugging in the values, we get a total power of 2.8*10^-7 W. This power represents the energy dissipated in the copper due to the incident plane wave.

I hope this helps. Let me know if you have any further questions. Good luck with your calculations!
 

1. What are depth problems in electromagnetics?

Depth problems in electromagnetics refer to the analysis of electromagnetic fields and their behavior within a medium or material at different depths or distances from the source. This is important in understanding the propagation of electromagnetic waves and their interactions with various materials.

2. How are depth problems solved in electromagnetics?

Depth problems are typically solved using mathematical and computational methods, such as the finite difference method or finite element method. These methods involve breaking down the problem into smaller, solvable parts and using numerical techniques to find solutions at different depths.

3. What factors affect the depth of an electromagnetic field?

The depth of an electromagnetic field is affected by several factors, including the frequency of the electromagnetic wave, the properties of the medium it is traveling through, and the size and shape of any objects present in the medium. These factors can all impact the strength and behavior of the field at different depths.

4. Why is understanding depth important in electromagnetics?

Understanding depth is crucial in electromagnetics as it allows us to predict and control the behavior of electromagnetic fields in different materials. This has many practical applications, such as in telecommunications, medical imaging, and materials engineering.

5. What are some common applications of depth problems in electromagnetics?

Depth problems in electromagnetics have a wide range of applications, including radar and sonar technology, geophysical prospecting, and subsurface imaging. They are also important in designing and optimizing antennas, waveguides, and other components used in various electronic devices.

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