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QJEEM19Ph1589: JEE Main 2019 Physics - Class 12 JEEM19Ph1589 Solution: The electric field of a plane polarized electromagnetic wave in …

The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by an expression E→(x,y)=10j^cos⁡[(6x+8z)].\overrightarrow E \left( {x,y} \right) = 10\widehat j\cos \left[ {\left( {6x + 8z} \right)} \right]. The magnetic field B→\overrightarrow B (x,z, t) is given by −- (c is the velocity of light)

Multiple Choice Options

  • A 1c(6k^+8i^)cos⁡[(6x+8z−10ct)]{1 \over c}\left( {6\hat k + 8\widehat i} \right)\cos \left[ {\left( {6x + 8z - 10ct} \right)} \right]
  • B 1c(6k^−8i^)cos⁡[(6x+8z−10ct)]{1 \over c}\left( {6\widehat k - 8\widehat i} \right)\cos \left[ {\left( {6x + 8z - 10ct} \right)} \right]
  • C 1c(6k^+8i^)cos⁡[(6x−8z+10ct)]{1 \over c}\left( {6\hat k + 8\widehat i} \right)\cos \left[ {\left( {6x - 8z + 10ct} \right)} \right]
  • D 1c(6k^−8i^)cos⁡[(6x−8z+10ct)]{1 \over c}\left( {6\hat k - 8\widehat i} \right)\cos \left[ {\left( {6x - 8z + 10ct} \right)} \right]

Step-by-Step Verified Solution

E→=10j^cos⁡[(6i^+8k^).(xi^+zk^)]\overrightarrow E = 10\widehat j\cos \left[ {\left( {6\widehat i + 8\widehat k} \right).\left( {x\widehat i + z\widehat k} \right)} \right]

=10j^ cos⁡[K→.r→]= 10\widehat j\,\cos \left[ {\overrightarrow K .\overrightarrow r } \right]

∴\therefore     K→=6i^+8k^;\overrightarrow K = 6\widehat i + 8\widehat k; direction of waves travel.

i.e., direction of 'c'.

JEE Main 2019 (Online) 10th January Evening Slot Physics - Electromagnetic Waves Question 122 English Explanation

∴\therefore    Direction of B^\widehat B will be along

C^×E^=−4i^+3k^5\widehat C \times \widehat E = {{ - 4\widehat i + 3\widehat k} \over 5}

Mag. of B→\overrightarrow B will be along

C^×E^=−4i^+3k^5\widehat C \times \widehat E = {{ - 4\widehat i + 3\widehat k} \over 5}

Mag. of B→=EC=10C\overrightarrow B = {E \over C} = {{10} \over C}

∴\therefore     B→=10C(−4i^+3k^5)=(−8i^+6k^)C\overrightarrow B = {{10} \over C}\left( {{{ - 4\widehat i + 3\widehat k} \over 5}} \right) = {{\left( { - 8\widehat i + 6\widehat k} \right)} \over C}

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