AP EAMCET · PHYSICS · Electromagnetic Waves

The electric field $(E)$ and magnetic field $(B)$ of an electromagnetic wave passing through vacuum are given by
$E = E_{0} \sin (k x - ω t)$
$B = B_{0} \sin (k x - ω t)$
Then the correct statement among the following is

A $E_{0} k = B_{0} ω$
B $E_{0} ω = B_{0} k$
C $E_{0} B_{\circ} = ω k$
D $E_{0} B_{0} = \frac{ω}{k}$

Verified Solution

Answer & Solution

Correct Answer

(A) $E_{0} k = B_{0} ω$

Step-by-step Solution

Detailed explanation

We know that the speed of a wave is given by, v=ωk ...i and the speed of the electromagnetic wave in vacuum is given by, c=E0B0 ...(ii) So, the speed of the electromagnetic wave, using i and ii is, ωk=E0B0 ⇒E0k=B0ω.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The electric field E and magnetic field B of an electromagnetic wave passing through vacuum are given byE=E0sinkx-ωtB=B0sinkx-ωtThen the correct statement among the following is

Step-by-step Solution

The electric field $(E)$ and magnetic field $(B)$ of an electromagnetic wave passing through vacuum are given by
$E = E_{0} \sin (k x - ω t)$
$B = B_{0} \sin (k x - ω t)$
Then the correct statement among the following is