Q: Which of the following is a correct expression for the Poynting vector $$\vec{S} in $$terms of $$\vec{E}$$ and $$\vec{B}$$?

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

Question 1

Which of the following best describes Maxwell's equations in free space?

Accepted Answer

They describe the behavior of electric and magnetic fields in the absence of charges and currents.

Question 2

According to Maxwell's equations, what is the relationship between the speed of electromagnetic waves $$c$$, the permittivity of free space $$\$$varepsilon_0$$, and the permeability of free space $$\$$mu_0$$?

Accepted Answer

$$c = \dfrac{1}{\sqrt{\$$varepsilon_0$$ \mu_0$}}$$

Question 3

Which equation represents the energy density $$u of an $$electromagnetic wave?

Accepted Answer

$$u = \dfrac{1}{2} \$$varepsilon_0$$ E^2$ + \dfrac{1}{2} \dfrac{B^2$}{\mu_0$}$$

Question 4

A plane electromagnetic wave is traveling in the $$+x$$ direction. If the electric field is given by $$E_y = E_{max} \sin(kx - \omega t)$$, what is the corresponding magnetic field $$B_z$$?

Accepted Answer

$$B_z = \dfrac{E_{max}}{c} \sin(kx - \omega t)$$

Question 5

What does the Poynting vector $$\vec{S}$$ represent in the context of electromagnetic waves?

Accepted Answer

The rate of energy transfer per unit area carried by the wave.

Question 6

If the average intensity $$I_{avg} of an $$electromagnetic wave is given by $$I_{avg} = \dfrac{c \$$varepsilon_0$$ E_{max}^2}{2}$$, what happens to the intensity if the amplitude of the electric field is doubled?

Accepted Answer

The intensity increases by a factor of 4.

Question 7

Which of the following is true about the relationship between the electric field $$\vec{E}$$ and magnetic field $$\vec{B} in a $$plane electromagnetic wave?

Accepted Answer

They are perpendicular to each other and to the direction of propagation.

Question 8

A radio station broadcasts at a frequency of $$100 	ext{ MHz}. $$What is the wavelength of the electromagnetic wave emitted? (Assume $$c = 3.00 	imes 10^8$ 	ext{ m/s})$$

Accepted Answer

$$\lambda = 3.00 	ext{ m}$$

Question 9

Which of the following best describes the energy flow in an electromagnetic wave?

Accepted Answer

Energy is carried by both the electric and magnetic fields and flows in the direction of wave propagation.

Question 10

If the electric field in a plane electromagnetic wave is described by $$E_y = E_{max} \sin(kx - \omega t)$$, what is the phase relationship between the electric and magnetic fields?

Accepted Answer

They are in phase with each other.

Question 11

A laser beam has an intensity of $$I = 1.0 	ext{ kW/m}^2. $$What is the magnitude of the maximum electric field $$E_{max} in $$the beam? (Use $$c = 3.00 	imes 10^8$ 	ext{ m/s}$$ and $$\$$varepsilon_0$$ = 8.85 	imes 10$$^{-12}$$ 	ext{ F/m})$$

Accepted Answer

$$E_{max} = 868 	ext{ V/m}$$

Question 12

Which of the following is a correct expression for the Poynting vector $$\vec{S} in $$terms of $$\vec{E}$$ and $$\vec{B}$$?

Accepted Answer

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

Question 13

If the magnetic field in a plane electromagnetic wave is $$B_{max} = 2.0 	imes 10$$^{-7}$$ 	ext{ T}$$, what is the maximum electric field $$E_{max}$$? (Use $$c = 3.00 	imes 10^8$ 	ext{ m/s})$$

Accepted Answer

$$E_{max} = 60 	ext{ V/m}$$

Question 14

Which of the following statements about electromagnetic waves is correct?

Accepted Answer

They can travel through a vacuum without any medium.

Question 15

A microwave oven operates at a frequency of $$2.45 	ext{ GHz}. $$What is the wavelength of the microwaves? (Use $$c = 3.00 	imes 10^8$ 	ext{ m/s})$$

Accepted Answer

$$\lambda = 0.122 	ext{ m}$$

Question 16

Which of the following best describes the polarization of an electromagnetic wave?

Accepted Answer

The orientation of the electric field vector.

Question 17

If the energy density of an electromagnetic wave is $$u = \$$varepsilon_0$$ E^2$, what is the total energy in a volume V$?

Accepted Answer

$$U = \$$varepsilon_0$$ E^2$ V$$

Question 18

A solar panel receives sunlight with an average intensity of $$I = 1.0 	ext{ kW/m}^2. $$What is the average energy delivered to a $$2.0 	ext{ m}^2$$ panel in $$10$$ seconds?

Accepted Answer

$$2.0 	imes 10^4$ 	ext{ J}$$

Question 19

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

Accepted Answer

They require a medium to propagate.

Chapter 32: Electromagnetic Waves – Summary and Key Concepts

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