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When the Maxwell equation is expressed in frequency domain, then which substitution is possible?
- a)d/dt = w/j
- b)d/dt = j/w
- c)d/dt = jw
- d)Expression in frequency domain is not possible
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
When the Maxwell equation is expressed in frequency domain, then which...
Answer: c
Explanation: The conversion of time to frequency domain in Maxwell equation is given by the Fourier Transform. Differentiation in time gives jw in frequency domain. Thus d/dt = jw in frequency domain.
Explanation: The conversion of time to frequency domain in Maxwell equation is given by the Fourier Transform. Differentiation in time gives jw in frequency domain. Thus d/dt = jw in frequency domain.
Most Upvoted Answer
When the Maxwell equation is expressed in frequency domain, then which...
Maxwell's equations are a set of four partial differential equations that describe the behavior of electromagnetic fields. When these equations are expressed in the frequency domain, they are commonly used to analyze the behavior of circuits and systems that operate at specific frequencies.
Substitution in Frequency Domain:
In the frequency domain, time derivatives are replaced by complex exponential functions. To express the Maxwell equation in the frequency domain, we use the following substitution:
d/dt = jw
Here, j is the imaginary unit and w is the angular frequency. This substitution is possible because in the frequency domain, the time derivative of a sinusoidal function is proportional to the frequency of the function.
Maxwell Equations in Frequency Domain:
Using the above substitution, we can express the Maxwell equations in the frequency domain as follows:
1. Gauss's Law for Electric Fields:
∇ · E = ρ/ε0
∇ · E = jwρ/ε0
2. Gauss's Law for Magnetic Fields:
∇ · B = 0
∇ · B = 0
3. Faraday's Law:
∇ × E = -dB/dt
∇ × E = -jwB
4. Ampere's Law:
∇ × B = μ0(jρ + ε0(dE/dt))
∇ × B = μ0j(ρ + ε0jwE)
Conclusion:
In the frequency domain, the substitution d/dt = jw is used to express the Maxwell equation. This substitution is possible because in the frequency domain, time derivatives are replaced by complex exponential functions.
Substitution in Frequency Domain:
In the frequency domain, time derivatives are replaced by complex exponential functions. To express the Maxwell equation in the frequency domain, we use the following substitution:
d/dt = jw
Here, j is the imaginary unit and w is the angular frequency. This substitution is possible because in the frequency domain, the time derivative of a sinusoidal function is proportional to the frequency of the function.
Maxwell Equations in Frequency Domain:
Using the above substitution, we can express the Maxwell equations in the frequency domain as follows:
1. Gauss's Law for Electric Fields:
∇ · E = ρ/ε0
∇ · E = jwρ/ε0
2. Gauss's Law for Magnetic Fields:
∇ · B = 0
∇ · B = 0
3. Faraday's Law:
∇ × E = -dB/dt
∇ × E = -jwB
4. Ampere's Law:
∇ × B = μ0(jρ + ε0(dE/dt))
∇ × B = μ0j(ρ + ε0jwE)
Conclusion:
In the frequency domain, the substitution d/dt = jw is used to express the Maxwell equation. This substitution is possible because in the frequency domain, time derivatives are replaced by complex exponential functions.
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When the Maxwell equation is expressed in frequency domain, then which substitution is possible?a)d/dt = w/jb)d/dt = j/wc)d/dt = jwd)Expression in frequency domain is not possibleCorrect answer is option 'C'. Can you explain this answer?
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