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Suppose a source of electromagnetic waves radiates uniformly in all directions in empty space where there are no absorption or interference effects. (a) Show that the intensity is inversely proportional to r2, the distance from the source squared. (b) Show that the magnitudes of the electric and magnetic fields are inversely proportional to r .

Short Answer

Expert verified

(a) The intensity is found to be inversely proportional tor2 .

(b) BothB0 andE0 are proportionate to 1r.

Step by step solution

01

Define electromagnetic waves

Electromagnetic waves, or EM waves, are waves that are formed when an electric field and a magnetic field vibrate together.

02

Explanation

(a)

The power transferred per unit area is defined as the wave's intensity, which is provided by

I=PAI=P4ฯ„ฯ„r2

Or

role="math" localid="1655961116164" Iโˆ1r2

As a result, the intensity is found to be inversely proportional to r2.

03

Explanation

(b)

The formula also gives intensity in terms of electric field and light speed

I=cฮต0E022AlsoI=p4ฯ„ฯ„r2Equateboththeequations,

cฮต0E022=p4ฯ„ฯ„r2E02=P2ฯ„ฯ„r2cฮต0E0=p2ฯ„ฯ„r2cฮต0E0โˆ1rAlso,fromthemagneticfieldandelectricfieldrelationship,cB0=E0B0โˆE0B0โˆ1rAsaresult,bothB0andE0areproportionateto1r.

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