Q: Which equation correctly relates the Poynting vector $$\vec{S} to $$the electric and magnetic fields in an EM wave?

$$\vec{S} = \frac{1}{\mu_0$} \vec{E} \times \vec{B}$$

Question 1

Which of the following statements about electromagnetic (EM) waves is correct?

Accepted Answer

EM waves have no mass and travel with velocity $$c in a $$vacuum.

Question 2

The Poynting vector $$\vec{S}$$ represents which physical quantity?

Accepted Answer

The energy per unit time per unit area carried by an EM wave.

Question 3

A 100 W light bulb radiates EM energy isotropically. If 10% of the power is visible light, what is the intensity of visible light 2 m from the bulb?

Accepted Answer

$$I = \frac{10}{4\pi (2)^2$} = 0.20\ \mathrm{W/m^2$}$$

Question 4

Which equation correctly relates the Poynting vector $$\vec{S} to $$the electric and magnetic fields in an EM wave?

Accepted Answer

$$\vec{S} = \frac{1}{\mu_0$} \vec{E} 	imes \vec{B}$$

Question 5

What is the radiation pressure exerted on a perfectly absorbing surface by an EM wave of intensity $$I$$?

Accepted Answer

$$P = \frac{I}{c}$$

Question 6

How are electromagnetic waves produced?

Accepted Answer

By accelerating electric charges.

Question 7

The energy density $$u of an EM $$wave is given by which of the following expressions?

Accepted Answer

$$u = \$$epsilon_0$$ E^2$

Question 8

A NASA solar sail has an area of $$80\ \mathrm{m^2$}$$ and mass $$30\ \mathrm{kg}. If $$the solar constant is $$1360\ \mathrm{W/m^2$}$$, what is the acceleration of the sail due to radiation pressure (assume perfect absorption)?

Accepted Answer

$$a = \frac{I A}{m c}$$

Question 9

Which of the following best describes the intensity $$I of an EM $$wave from an isotropic point source at distance $$r$$?

Accepted Answer

$$I \propto \frac{1}{r^2$}$$

Question 10

Which of the following is a correct expression for the speed of light $$c in $$terms of the vacuum permittivity $$\$$epsilon_0$$ and permeability $$\$$mu_0$$?

Accepted Answer

$$c = \frac{1}{\sqrt{\$$epsilon_0$$ \mu_0$}}$$

Question 11

A half-wave (Hertz) antenna is commonly used for which frequency range?

Accepted Answer

From 3 kHz to 3 GHz

Question 12

If the electric field amplitude of a plane EM wave is doubled, what happens to the intensity $$I$$?

Accepted Answer

It is quadrupled.

Question 13

Which of the following is NOT a property of EM waves?

Accepted Answer

They require a medium to propagate.

Question 14

What is the correct formula for the time-averaged intensity $$I of an EM $$wave in terms of the maximum electric field $$E_0$$ and constants?

Accepted Answer

$$I = \frac{c \$$epsilon_0$$ E_0$^2}{2}$$

Question 15

Which of the following best describes the relationship between the electric and magnetic fields in a plane EM wave?

Accepted Answer

$$E = cB$$

Question 16

A dipole antenna emits EM waves. What is the primary mechanism for the generation of these waves?

Accepted Answer

Oscillating electric charges in the antenna.

Question 17

If the intensity of sunlight at Earth's distance from the Sun is $$1360\ \mathrm{W/m^2$}$$, what is the radiation pressure on a perfectly reflecting solar sail?

Accepted Answer

$$P = \frac{2I}{c}$$

Question 18

Which of the following is true about the energy carried by EM waves?

Accepted Answer

It is stored in both the electric and magnetic fields.

Question 19

Which equation gives the average power $$\langle P \rangle$$ radiated through a sphere of radius $$r by an $$isotropic source?

Accepted Answer

$$\langle P \rangle = I (4 \pi r^2$)$$

Electromagnetic Waves: Energy, Momentum, and Production

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