Choose the correct answer from the alternatives given-Poynting vectors S- is defined as S- 1-0E-B- the average value of -S-over a single period -T-is given by

The correct option is B E_0^2/2cμ_o Poynting vector is given by, S⃗=E⃗×B⃗ #956;_0 Average value of magnitude of radiant flux density over one cycle ...

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Standard XII

Mathematics

Theorems for Continuity

Choose the co...

Question

Choose the correct answer from the alternatives given.
Poynting vectors $\to S$ is defined as $\to S = \frac{1}{μ_{0}} \to E \times \to B$ . the average value of $^{'}^{'}$ over a single period 'T'is given by

E_{0}^{2} / 2 c μ_{o}

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E_{0}^{2} / c μ_{o}

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2 E_{0}^{2} / c μ_{o}

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E_{0}^{2} / c μ_{o}^{2}

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Solution

The correct option is B $E_{0}^{2} / 2 c μ_{o}$
Poynting vector is given by, $\to S = \frac{\to E \times \to B}{μ_{0}}$

Average value of magnitude of radiant flux density over one cycle is
$S_{a v} = \frac{1}{μ_{0}} ∣_{0} \times_{0} | (\frac{1}{T}) \int_{0}^{T} c o s^{2} (k x - ω t) d t$

$[∵ E = E_{0} c o s (k x - ω t), B = B_{0} c o s (k x - ω t)]$

$= \frac{E_{0} B_{0}}{μ_{0}} (\frac{1}{T}) (\frac{T}{2})$

$= \frac{E_{0} B_{0}}{2 μ_{0}}$ $[∵ \int_{0}^{T} c o s^{2} (k x - ω t) d t = \frac{T}{2}]$

$S_{a v} = \frac{E_{0} (E_{0} / c)}{2 μ 0} = (\frac{1}{2 c μ_{0}}) E_{0}^{2} (∵ B_{0} = \frac{E_{0}}{c})$

So, option $(A)$ is correct

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Choose the correct answer from the alternatives given.Poynting vectors →S is defined as →S=1μ0→E×→B. the average value of ′→S′over a single period 'T'is given by

Choose the correct answer from the alternatives given.
Poynting vectors $\to S$ is defined as $\to S = \frac{1}{μ_{0}} \to E \times \to B$ . the average value of $^{'}^{'}$ over a single period 'T'is given by