For a plane electromagnetic wave propagating in <math> <mi mathvariant="normal">x</mi> </math> -direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively? &lt;!-- [if !supportLineBreakNewLine]--&gt; &lt;!--[endif]--&gt;

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Physics Class 12th Physics Electromagnetic Waves

For a plane electromagnetic wave propagating in $x$ -direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively?

Option 1 -

$\hat{j} + \hat{k}, \hat{j} + \hat{k}$

Option 2 -

$- \hat{j} + \hat{k}, - \hat{j} - \hat{k}$

Option 3 -

$\hat{j} + \hat{k}, - \hat{j} - \hat{k}$

Option 4 -

$- \hat{j} + \hat{k}, - \hat{j} + \hat{k}$

2 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

$\overset{?}{v} ? \overset{?}{E} \times \overset{?}{B}, \hat{v} = \hat{i}$

Option (1) $\overset{?}{E} \times \overset{?}{B} = \overset{?}{0} \overset{?}{E} ? \overset{?}{B}$

Option (2) $\overset{?}{E} \times \overset{?}{B} = 2 \hat{i}$ parallel to $\overset{?}{v}$

Option (2) $\overset{?}{E} \times \overset{?}{B} = \overset{?}{0} \overset{?}{E} ⇑ \overset{?}{B}$

Option (2) $\overset{?}{E} \times \overset{?}{B} = \overset{?}{0} \overset{?}{E} ? \overset{?}{B}$

<math> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">v</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>? </mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>×</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>, </mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">v</mi> </mrow> </mrow> <mi mathvariant="normal">ˆ</mi> </mover> <mo>=</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </mrow> <mi mathvariant="normal">ˆ</mi> </mover> </math> <!- [endif]-><!- [endif]->Option (1) <math> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>×</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>=</mo> <mover accent="true"> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> <mo>? </mo> </mover> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>? </mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> <!- [endif]-><!- [endif]->Option (2) <math> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>×</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>=</mo> <mn>2</mn> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </mrow> <mi mathvariant="normal">ˆ</mi> </mover> </math> parallel to <math> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">v</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> <!- [endif]-><!- [endif]->Option (2) <math> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>×</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>=</mo> <mover accent="true"> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> <mo>? </mo> </mover> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>⇑</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> <!- [endif]-><!- [endif]->Option (2) <math> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>×</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>=</mo> <mover accent="true"> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> <mo>? </mo> </mover> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>? </mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> <!- [endif]-><!- [endif]->

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For a plane electromagnetic wave propagating in $x$ -direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively?