Electromagnetic Waves — Practice

Question 1

A radio station broadcasts at 100 MHz. Find the wavelength of the wave in air.

Accepted Answer

Use c = nu lambda, taking c as 3 x 10^8 m/s. Answer: lambda = 3.0 m.

Question 2

The magnetic field amplitude of an electromagnetic wave in vacuum is 2.0 x 10^-7 T. Find the electric field amplitude.

Accepted Answer

Apply E_0 = c B_0, which follows from Maxwell's equations. Answer: E_0 = 60 N/C.

Question 3

Arrange radio waves, X-rays, infrared and ultraviolet in order of increasing frequency, and state which carries the most energy per photon.

Accepted Answer

Frequency rises as wavelength falls, and photon energy follows E = h nu. Answer: Radio, infrared, ultraviolet, X-rays; X-rays carry the most energy per photon.

Question 4

A parallel plate capacitor of capacitance 20 pF is charged so that the voltage across it rises at 5.0 x 10^9 V/s. Find the displacement current between the plates.

Accepted Answer

The displacement current equals the conduction current, which is C times the rate of change of voltage. Answer: i_d = 0.1 A.

Question 5

A plane electromagnetic wave has frequency 3.0 x 10^10 Hz. Find its wavelength, angular frequency and propagation constant in vacuum.

Accepted Answer

Apply c = nu lambda, then omega = 2 pi nu and k = omega/c. Answer: lambda = 1.0 cm; omega = 1.9 x 10^11 rad/s; k = 628 rad/m.

Question 6

Find the photon energy in electronvolts for visible light of wavelength 500 nm.

Accepted Answer

First find the frequency from c = nu lambda, then apply E = h nu and convert joules to electronvolts. Answer: E = 2.5 eV approximately.

Question 7

An electromagnetic wave in vacuum has electric field amplitude 60 V/m. Find the average energy densities of the electric and magnetic fields and show they are equal.

Accepted Answer

Use u_E = half epsilon_0 E squared and u_B = B squared over 2 mu_0, averaging the square of a sinusoid to half its peak, then substitute B_0 = E_0/c. Answer: Both equal about 8.0 x 10^-9 J per cubic metre.

Question 8

A capacitor with circular plates of radius 8.0 cm is being charged, with the electric field between the plates rising at 2.0 x 10^12 V/m per second. Find the displacement current.

Accepted Answer

Form the electric flux as E times the plate area, then apply i_d = epsilon_0 times its rate of change. Answer: i_d = 0.36 A.

Question 9

A plane electromagnetic wave travels along the positive x-direction with its electric field along the y-direction. State the direction of the magnetic field, and explain why the wave is called transverse.

Accepted Answer

The direction of travel is along E cross B, so work backwards to place B, then compare the field directions with the propagation direction. Answer: B is along the z-direction; both fields are perpendicular to the direction of travel, which is what transverse means.

Practice — Electromagnetic Waves

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