Finding the Frequency Domain and Time Domain magnetic field

In summary, the conversation discusses how to better understand the solutions for two given questions. The solution involves using Faraday's law in differential form and calculating the curl of E to find B. The conversation also mentions that H may be missing a factor and part (c) can be answered by analyzing the relationship between the magnetic field, electric field, and direction of propagation in a plane wave in free space.
  • #1
EmmanKR
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Thread moved from the technical forums to the schoolwork forums
I was wondering if anyone could walk me though a better explanation on how to get the given results for these two questions. The solutions posted by my professor aren't really clear to me so if anyone is able to better explain how to get the solution it would be much appreciated!
 

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  • #2
For c) You should use Faraday's law in differential form $$\nabla\times\mathbf{E}=-\frac{d\mathbf{B}}{dt}\Rightarrow \mathbf{B}=-\int \nabla\times\mathbf{E} dt$$
You know E in explicit form so you can calculate its curl and then calculate the time integral to get B.
Your handwriting is pretty bad but I think your expression for H is missing a ##\frac{1}{c}## factor.
 
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  • #3
You should be able to answer part (c) almost by inspection. You have a plane wave in free space. How are the magnetic field, the electric field, and the direction the wave propagates related?
 

1. What is the difference between the frequency domain and time domain magnetic field?

The frequency domain magnetic field refers to the representation of the magnetic field in terms of its frequency components. In contrast, the time domain magnetic field refers to the representation of the magnetic field in terms of its amplitude and time. Essentially, the frequency domain provides information about the different frequencies present in the magnetic field, while the time domain provides information about the behavior of the magnetic field over time.

2. How do you convert a magnetic field from the time domain to the frequency domain?

To convert a magnetic field from the time domain to the frequency domain, you can use a mathematical operation called a Fourier transform. This transforms the time domain signal into its frequency components, allowing for analysis of the different frequencies present in the magnetic field.

3. What are the practical applications of analyzing the frequency domain and time domain magnetic field?

Analyzing the frequency domain and time domain magnetic field can provide valuable information for a variety of applications. For example, in the field of medical imaging, analyzing the frequency domain magnetic field can help identify abnormalities in the brain or other organs. In the field of telecommunications, analyzing the frequency domain magnetic field can help improve signal processing and transmission. Additionally, understanding the behavior of the magnetic field in both domains can aid in the design and optimization of electrical devices.

4. Are there any limitations to analyzing the frequency domain and time domain magnetic field?

While analyzing the frequency domain and time domain magnetic field can provide valuable insights, there are some limitations to consider. For example, the accuracy of the analysis may be affected by external factors such as noise or interference. Additionally, the analysis may be limited by the capabilities of the equipment used to measure the magnetic field.

5. How does the magnetic field change over time in the frequency domain?

In the frequency domain, the magnetic field is represented by a spectrum that shows the amplitude of each frequency component. This spectrum can change over time as the magnetic field is influenced by external factors or as the source of the magnetic field changes. By analyzing these changes, scientists can gain a better understanding of the behavior and characteristics of the magnetic field.

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