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Chapter 31: Q. 19 (page 901)

A helium-neon laser emits a $1.0$ -mm-diameter laser beam with a power of $1.0 m W$ . What are the amplitudes of the electric and magnetic fields of the light wave?

Short Answer

Expert verified

The amplitudes of the light wave's electric and magnetic fields is,

$\begin{array}{l} E_{o} = 976 V / m, \\ B_{o} = 3.3 μ T . \end{array}$

Step by step solution

01

Step: 1 Finding the values of Iavg:

Finding the world first

$A = π \times r^{2} A = π {(10^{- 3})}^{2} A = π \times 10^{- 6} .$

Then finding the values

$\begin{array}{l} I_{a v g} = \frac{P}{A} \\ I_{a v g} = \frac{10^{- 3}}{π \times 10^{- 6}} \\ I_{a v g} = 1.27 \times 10^{3} . \end{array}$

02

Step: 2 Finding the vales of E0:

By using the formula,

$E_{o} = {(\frac{2 I_{a v g}}{c \cdot ε_{o}})}^{1 / 2} \begin{array}{l} E_{o} = {(\frac{2 I_{a v g}}{c \cdot ε_{o}})}^{1 / 2} \\ E_{o} = {(\frac{2 \times 1.27 \times 10^{3}}{3 \times 10^{8} \times 8.85 \times 10^{- 12}})}^{1 / 2} \\ E_{o} = 976 V / m . \end{array}$

03

Step: 3 Finding the values of B0:

By using,

$\begin{array}{l} B_{o} = \frac{E_{o}}{c} \\ B_{o} = \frac{976}{3 \times 10^{8}} \\ B_{o} = \frac{9.7 \times 10^{2}}{3 \times 10^{8}} \\ B_{o} = 3.3 μ T . \end{array}$

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Most popular questions from this chapter

$F I G U R E P 31.39$ Shows the electric field inside a cylinder of radius localid="1649879543758" $R = 3.0 m m .$ . The field strength is increasing with time as localid="1649879549377" $E = 1.0 \times 10^{8} t^{2} V / m$ , where $t$ is in $s$ . The electric field outside the cylinder is always zero, and the field inside the cylinder was zero for localid="1649879554833" $t < 0$ .

localid="1649879566359" $a .$ Find an expression for the electric flux localid="1649879560575" $ϕ_{e}$ through the entire cylinder as a function of time.

localid="1649879572467" $b$ . Draw a picture showing the magnetic field lines inside and outside the cylinder. Be sure to include arrowheads showing the field’s direction.

localid="1649879587867" $c$ . Find an expression for the magnetic field strength as a function of time at a distance localid="1649879577475" $r < R$ from the center. Evaluate the magnetic field strength atlocalid="1649879582437" $r = 2.0 m m$ , localid="1649879592577" $t = 2.0 s$ .

d. Find an expression for the magnetic field strength as a function of time at a distancelocalid="1649879597467" $r > R$ from the center. Evaluate the magnetic field strength at localid="1649879602321" $r = 4.0 m m$ , localid="1649879607075" $t = 2.0 s$ .

The magnetic field is uniform over each face of the box shown in $F I G U R E E X 31.6 .$ What are the magnetic field strength and direction on the front surface?

a. What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is $100 V / m$ $?$

b. What is the intensity of the wave $?$

In what directions are the electromagnetic waves traveling in FIGURE

What is the force (magnitude and direction) on the proton in FIGURE P31.29? Give the direction as an angle $CW$ or $cCW$ from vertical.

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