Tutorials in Introductory Physics
Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 23.4, Problem 1aTH

A long, thin steel wire is cut in half, and each half is connected to a different terminal of a light bulb. An electromagnetic (EM) plane wave ( E ( x , y , z , t ) = E o sin ( k x ω t ) y ^ , B ( x , y , z , t ) = B o sin ( k x ω t ) z ^ ) moves past the wire, as shown.

Chapter 23.4, Problem 1aTH, A long, thin steel wire is cut in half, and each half is connected to a different terminal of a

    a. In what direction is the wave propagating? Explain your reasoning.

Expert Solution & Answer
Check Mark
To determine

The direction of the propagation of the wave.

Answer to Problem 1aTH

The direction of the propagation of the wave is along positive x axis.

Explanation of Solution

Introduction:

An electromagnetic wave is shown graphically as below:

  Tutorials in Introductory Physics, Chapter 23.4, Problem 1aTH

Figure 1: An electromagnetic wave

The given electric field is in the form of sinusoidal wave form is:

  E(x,y,z,t)=EoSin(kxωt)y^

According to the above equation, the direction of oscillating electrical field is along y and the direction of the wave propagation is along x direction. The corresponding magnetic field is given as below:

  B(x,y,z,t)=BoSin(kxωt)z^

The magnetic field (black dotted sine wave) and electric field (red dotted sine wave) are shown in Figure 1.

The direction of the electromagnetic wave can be determined by the argument of the function, here is the Sin function which is kxωt which is constant.

  kxωt=constant.(1)

  k is the propagation constant, x is the direction of propagation, ω is the angular frequency.

Derivative of this equation 1

  kdxdtω=0dxdt=ωk=v=positive

The speed ωk=v is positive, hence wave is propagating along positive x axis.

Conclusion:

The direction of the propagation of the wave is along positive x axis.

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