An electromagnetic wave is represented by the electric field E-E0n- sin- t-6y-8z- Taking unit vectors in x y and z directions to be -k- the direction of propogation - is given by-

E=E_0 n̂sin[ω t+ s·r] Comparing this with the given equation, s·r =6y 8z=6ĵ 8k̂· (xî+yĵ+zk̂) ⇒s =6ĵ 8k̂ Thus, ŝ=s|s|=35ĵ 45k̂ Hence, option (B) is the corr ...

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Standard XII

Physics

Different Forms of Equations

An electromag...

Question

An electromagnetic wave is represented by the electric field $\to E = E_{0}^n sin [ω t + (6 y - 8 z)]$ Taking unit vectors in $x y$ and $z$ directions to be $^i,^j,^k$ , the direction of propogation $^s$ is given by:

^s = \frac{- 4^k + 3^j}{5}

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^s = \frac{2^j - 3^k}{5}

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^s = (\frac{- 3^j + 4^k}{5})

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^s = \frac{3^i - 4^j}{5}

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Solution

The correct option is A $^s = \frac{- 4^k + 3^j}{5}$
$\to E = E_{0}^n sin [ω t + \to s \cdot \to r]$

Comparing this with the given equation,

$\to s \cdot \to r = 6 y - 8 z = 6^j - 8^k \cdot (x^i + y^j + z^k)$

$\Rightarrow \to s = 6^j - 8^k$

Thus, $^s = \frac{\to s}{| s |} = \frac{3}{5}^j - \frac{4}{5}^k$

Hence, option (B) is the correct answer.

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An electromagnetic wave is represented by the electric field →E=E0^n sin[ωt+(6y−8z)] Taking unit vectors in x y and z directions to be ^i,^j,^k, the direction of propogation ^s is given by:

The correct option is A ^s=−4^k+3^j5→E=E0^nsin[ωt+→s⋅→r] Comparing this with the given equation, →s⋅→r=6y−8z=6^j−8^k⋅(x^i+y^j+z^k) ⇒→s=6^j−8^k Thus, ^s=→s|s|=35^j−45^k Hence, option (B) is the correct answer.

An electromagnetic wave is represented by the electric field $\to E = E_{0}^n sin [ω t + (6 y - 8 z)]$ Taking unit vectors in $x y$ and $z$ directions to be $^i,^j,^k$ , the direction of propogation $^s$ is given by: