GATE EC 2020 Set 1 — Question 55
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Electromagnetics → Maxwell's Equations → Differential & Integral Forms
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Question
The magnetic field of a uniform plane wave in vacuum is given by
.
The value of is
.
The value of is
Correct answer
1 to 1
Solution
The given magnetic field of a uniform plane wave in vacuum is:
For a uniform plane wave, the propagation vector can be identified from the phase term. The phase is .
Comparing this with the general form , we have:
So, .In vacuum, the propagation constant , where is the speed of light in vacuum.
.
So, .For a uniform plane wave in a source-free region, the magnetic field must satisfy Maxwell's equations. One of the key properties is that the magnetic field is transverse to the direction of propagation . This means .Let be the amplitude vector of the magnetic field.
Then, .
.Another property is that (Gauss's law for magnetism).
For a plane wave, if , then .
For , we must have .
This confirms the condition used above.The value of is .The final answer is .
For a uniform plane wave, the propagation vector can be identified from the phase term. The phase is .
Comparing this with the general form , we have:
So, .In vacuum, the propagation constant , where is the speed of light in vacuum.
.
So, .For a uniform plane wave in a source-free region, the magnetic field must satisfy Maxwell's equations. One of the key properties is that the magnetic field is transverse to the direction of propagation . This means .Let be the amplitude vector of the magnetic field.
Then, .
.Another property is that (Gauss's law for magnetism).
For a plane wave, if , then .
For , we must have .
This confirms the condition used above.The value of is .The final answer is .
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