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A plane electromagnetic wave travels in ...

A plane electromagnetic wave travels in vacuum along z - direction. What can you say about the directions of its electric and magnetic field vectors ? If the frequency of the wave is 30 MHz, what is its wavelength ?

Text Solution

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Here `vec(E )` must be along + X axis and `vec(B)` must be along + Y axis, so that direction of `vec(E )xx vec(B)=` direction of `hat(i)xx hat(j)=` direction of `hat(k)=` direction of + Z axis = direction of propagation of electromagnetic wave.
In both of above cases, `vec(E )` and `vec(B)` will oscillate perpendicular to each other in XY - plane, perpendicular to direction of propagation of electromagnetic wave.
Since given electromagnetic wave propagates in vacuum, its speed would be equal to c. Now, according to formula,
`c=v lambda`
`therefore lambda = (c )/(v)=(3xx10^(8))/(30xx10^(6))=10m`
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Knowledge Check

  • A plane electromagnetic wave propagating along x - direction can have the following pairs of vec(E ) and vec(B) .

    A
    `E_(x), B_(y)`
    B
    `E_(y),B_(z)`
    C
    `B_(x),E_(y)`
    D
    `E_(z),B_(y)`

  • An electromagnetic wave travels in vacuum along z - direction : vec(E )=(E_(1)hat(i)+E_(2)hat(j))cos(kz-omega t) . Choose the correct options from the following :

    A
    The associated magnetic field is given as `vec(B)=(1)/(c )(E_(1)-E_(2)hat(j))cos (kz-omega t)`
    B
    The associated magnetic field is given as `vec(B)=(1)/(c )(E_(1)hat(i)+E_(2)hat(j))cos (kz-omega t)`
    C
    The given electromagnetic field is circularly polarised.
    D
    The given electromagnetic wave is plane polarised.

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