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Chapter 23: Q21 P (page 988)

A pulse of radiation propagates with velocity <0,0,-c>. The electric field in the pulse is <7.2×106,0,0>N/C. What is the magnetic field in the pulse?

Short Answer

Expert verified

The magnetic field in the pulse is <0,-0.024,0>T.

Step by step solution

01

Given data

Velocity of the pulse:

v→=0,0,-c

Electric field of the pulse:

E→=7.2×106,0,0N/C

02

Magnetic field in a pulse

Magnitude of magnetic field in a pulse with magnitude of electric field is:

B=Ec …… (i)

Here, is the speed of light in vacuum with value c=3×108m/sc=3×108m/s.

The direction of the magnetic field is such that the direction of the wave is given by the direction as follows:

E→×B→

03

Determine the magnetic field in the given pulse

From equation (i), the magnitude of the electric field is:

B=7.2×106N/C3×108m/s=0.024·1N.s/C.m×1T1N.s/C.m=0.024T

The direction of the wave is along -zaxis and the direction of the electric field is along x axis. Hence the direction of the magnetic field has to be along -yaxis.

Thus, the magnetic field is 0,-0.024,0T.

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Most popular questions from this chapter

An electric field of 1×106N/C acts on an electron, resulting in an acceleration of 1.8×1017m/s2 for a short time. What is the magnitude of the radiative electric field observed at a location a distance of 2cm away along a line perpendicular to the direction of the acceleration?

Calculate the wave length for several examples of sinusoidal electromagnetic radiation:

radio,1000kHz,λ=?

television,100MHz,λ=?

red light,4.3×1014Hz,λ=?

blue light,7.5×1014Hz,λ=?

(Note for comparison that an atomic diameter is about 1×10-10m,).

If a diver who is underwater shines a flashlight upward toward the surface, at an angle of 29° from the normal, at what angle does the light emerge from the water? The indices of refraction are: water,1.33 ; air,1.00029

A slab (pulse) of electromagnetic radiation that is 15cm thick is propagating downward (in the direction) toward a short horizontal copper wire located at the origin and oriented parallel to the z axis, as shown in Figure 23.123. (a) The direction of the electric field inside the slab is out of the page (in the+z direction). On a diagram, show and describe clearly the direction of the magnetic field inside the slab.

(b) You stand on the x axis at location<12,0,0>m, at right angles to the direction of propagation of the pulse. Your friend stands on the z axis at location<0,0,12>m. The pulse passes the copper wire at time t1=0, and at a later time t2 you observe new nonzero electric and magnetic fields at your location, but your friend does not. Explain. What is t2? (Give a numerical answer.) How long a time do these new fields last for you? (c) On a diagram, show and describe clearly the directions of these new nonzero fields (E→ and B→) at your location. Explain briefly but carefully.

What is the wavelength of ultraviolet light whose frequency is 5×1015Hz?
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