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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-direction6 × 10

^{-8}T along the x-direction6 × 10

^{-8}T along the z-direction2 × 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`

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