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  • I have a doubt, kindly clarify. The electric and the magnetic field associated with an E.M. wave, propagating along the +z-axis, can be represented by

The electric and the magnetic field associated with an E.M. wave, propagating along the +z-axis, can be represented by

 

  • Option 1)

    [\Vec{E}=E_{0} \hat{i}, \Vec {B}=B_{0}\hat{j}]

  • Option 2)

    [\Vec{E}=E_{0} \Vec{k}, \Vec {B}=B_{0}\hat{i}]

  • Option 3)

    [\Vec{E}=E_{0} \hat{j}, \Vec {B}=B_{0}\hat{i}]

  • Option 4)

    [\Vec{E}=E_{0} \hat{j}, \Vec {B}=B_{0}\hat{k}]

 

Answers (1)

 

Wave Equation -

E= E_{o} Sin w (t -frac{x}{c})

E is in y-z plane

- wherein

E - Electric field at (x,t)

Eo - Electric field amplitude

w= Angular frequency

c= Speed of light in vacuum 

 

 

Wave Equation -

B=B_{o} Sinw (t-frac{x}{c})

B is in y-z plane

- wherein

B = Magnetic field at (x,t)

Bo = Magnetic field amplitude

w = Angular frequency

c = Speed of light in vacuum

 

 \underset{E}{\rightarrow}\:and\: \underset{B}{\rightarrow} are mutually perpendicular and these two are perpendicular to direction of propogation (i.e. Z axis)

\therefore \underset{E}{\rightarrow}=E_{o}\hat{i}\:or\:E_{o}\hat{j}\:It\:follow\:\\ and \: \underset{B}{\rightarrow}=B_{o}\hat{j}\:or\:B_{o}(-\hat{i})\:right \:hand\:rule


Option 1)

[\Vec{E}=E_{0} \hat{i}, \Vec {B}=B_{0}\hat{j}]

This solution is correct 

Option 2)

[\Vec{E}=E_{0} \Vec{k}, \Vec {B}=B_{0}\hat{i}]

This solution is incorrect 

Option 3)

[\Vec{E}=E_{0} \hat{j}, \Vec {B}=B_{0}\hat{i}]

This solution is incorrect 

Option 4)

[\Vec{E}=E_{0} \hat{j}, \Vec {B}=B_{0}\hat{k}]

This solution is incorrect 

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subam

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