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Question -

In a plane electromagnetic wave,the electric field oscillates sinusoidally at a frequency of 2.0 ├Ч 1010┬аHz and amplitude 48 V mтИТ1.

(a)┬аWhat is the wavelength of the wave?

(b)┬аWhat is the amplitude of theoscillating magnetic field?

(c)┬аShow that the average energydensity of the┬аE┬аfieldequals the average energy density of the┬аB┬аfield. [c┬а= 3 ├Ч108┬аm sтИТ1.]



Answer -

Frequency of the electromagneticwave,┬а╬╜┬а= 2.0 ├Ч 1010┬аHz

Electricfield amplitude,┬аE0┬а= 48 V mтИТ1

Speed oflight,┬аc┬а= 3 ├Ч 108┬аm/s

(a)┬аWavelength of a wave is given as:

(b)┬аMagneticfield strength is given as:

(c)┬аEnergydensity of the electric field is given as:

And, energy density of themagnetic field is given as:

Where,

тИИ0┬а= Permittivity of free space

╬╝0┬а= Permeability offree space

We havethe relation connecting┬аE┬аand┬аB┬аas:

E┬а=┬аcB┬атАж (1)

Where,

┬атАж (2)

Puttingequation (2) in equation (1), we get

Squaring both sides, we get

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