A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E = 6 Vm-1 along the y-direction. - Physics (JEE Main)

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A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E = 6 Vm-1 along the y-direction. Its corresponding magnetic field component, B would be ______.

Options

  • 2 × 10-8 T along the z-direction

  • 6 × 10-8 T along the x-direction

  • 6 × 10-8 T along the z-direction

  • 2 × 10-8 T along the y-direction

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Solution

A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E = 6 Vm-1 along the y-direction. Its corresponding magnetic field component, B would be 2 × 10-8 T along the z-direction.

Explanation:

Given: An electromagnetic wave propagates along the x-axis, and the electric field component of the wave at a given point in space and time is

`vecE = 6V/m, hatj.`

To find: `vecB`, the magnetic field component associated with the given `vecE`.

For an electromagnetic wave: 

`|vecE|/|vecB| = c;`

`|vecB| = |vecE|/c = 6/(3 xx 10^8) = 2 xx 10^-8` T

Also, the direction of propagation of an EM wave = direction of `vecE` × direction of B, `hati = hatJ xx "direction of"  vecB`

That gives the direction of `vecB` along the z-axis.

The propagation direction of an electromagnetic wave is also equal to the direction of `vecE` the direction of `vecB`, and `hati = hatJ xx "direction of"  vecB.`

It indicates the `vecB` z-axis direction. 

So, `vecB = 2 xx 10^-8  hatk  T`

  Is there an error in this question or solution?

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