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Chapter 24: Q38PE (page 889)

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=P4蟿蟿谤2

Or

role="math" localid="1655961116164" I鈭�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=c蔚0E022AlsoI=p4蟿蟿谤2Equateboththeequations,

c蔚0E022=p4蟿蟿谤2E02=P2蟿蟿谤2肠蔚0E0=p2蟿蟿谤2肠蔚0E0鈭�1rAlso,fromthemagneticfieldandelectricfieldrelationship,cB0=E0B0鈭�E0B0鈭�1rAsaresult,bothB0andE0areproportionateto1r.

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Most popular questions from this chapter

The direction of the electric field shown in each part of the Figure 24.5is that produced by the charge distribution in the wire. Justify the direction shown in each part, using the Coulomb force law and the definition of E=F/q, where qis a positive test charge.

In which situation shown in Figure\({\rm{24}}{\rm{.24}}\)will the electromagnetic wave be more successful in inducing a current in the wire? Explain.

Can an antenna be any length? Explain your answer

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