Verified Solution • 2025–26 Session moderate

QJEEM20Phd914: JEE Main 2020 Physics - Class 12 JEEM20Phd914 Solution: In a plane electromagnetic wave, the directions of electric…

In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by k^\widehat k and 2i^−2j^2\widehat i - 2\widehat j , respectively. What is the unit vector along direction of propagation of the wave?

Multiple Choice Options

  • A 15(i^+2j^){1 \over {\sqrt 5 }}\left( {\widehat i + 2\widehat j} \right)
  • B 15(2i^+j^){1 \over {\sqrt 5 }}\left( {2\widehat i + \widehat j} \right)
  • C 12(i^+j^){1 \over {\sqrt 2 }}\left( {\widehat i + \widehat j} \right)
  • D 12(j^+k^){1 \over {\sqrt 2 }}\left( {\widehat j + \widehat k} \right)

Step-by-Step Verified Solution

E→×B→=k^×(2i^−2j^)\overrightarrow E \times \overrightarrow B = \widehat k \times \left( {2\widehat i - 2\widehat j} \right)

= 2k^×i^−2k^×j^2\widehat k \times \widehat i - 2\widehat k \times \widehat j

= (2j^+2i^)\left( {2\widehat j + 2\widehat i} \right)

Unit vector along E→×B→\overrightarrow E \times \overrightarrow B = (2j^+2i^)22{{\left( {2\widehat j + 2\widehat i} \right)} \over {2\sqrt 2 }}

= 12(i^+j^){1 \over {\sqrt 2 }}\left( {\widehat i + \widehat j} \right)

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