Q: A parallel-plate capacitor has an increasing electric potential difference across its plates. If $$\frac{d(\Delta V_c)}{dt} = 5.00 \times 10^5$ \ \frac{V}{s}$$, $$D = 5 \ \text{cm}$$, and $$d = 0.500 \ \text{mm}$$, what is the displacement current $$I_{disp}$$ between the plates?

$$1.74 \times 10$$^{-5}$$ \ \text{A}$$

Q: The speed of light in glass is $$2.00 \times 10^8$ \ \text{m/s}. $$What is the index of refraction of glass?

$$n = \frac{c}{v} = \frac{3.00 \times 10^8$}{2.00 \times 10^8$} = 1.50$$

Q: A Nd-YAG laser emits light with a wavelength of $$532 \ \text{nm} in $$vacuum. What is the frequency of this light?

$$f = \frac{c}{\lambda} = \frac{3.00 \times 10^8$}{532 \times 10$$^{-9}$$} = 5.64 \times 10$$^{14}$$ \ \text{Hz}$$

Q: A radio receiver can detect signals with electric field amplitudes as small as $$E_0 = 300$$ \ \mu\text{V/m}$$. What is the smallest detectable intensity?

$$I = \frac{c \$$epsilon_0$$}{2} E_0$^2 = 1.19 \times 10$$^{-10}$$ \ \text{W/m}^2$$

Q: Which of the following best describes the Poynting vector $$\vec{S}$$ for an electromagnetic wave?

$$\vec{S} = \frac{1}{\mu_0$} (\vec{E} \times \vec{B})$$, representing the energy flow per unit area per unit time.

Q: If an electromagnetic wave in vacuum has a magnetic field amplitude $$B_0 = 2.00$$ \ \text{mT}$$, what is the electric field amplitude E_0$?

$$E_0 = c$$ $$B_0 = 3.00$$ \times $$10^8$$ \times 2.00 \times $$10^{-3} = 6.00$$ \times $$10^5$$ \ \text{V/m}$$

Question 1

A parallel-plate capacitor has an increasing electric potential difference across its plates. If $$\frac{d(\Delta V_c)}{dt} = 5.00 	imes 10^5$ \ \frac{V}{s}$$, $$D = 5 \ 	ext{cm}$$, and $$d = 0.500 \ 	ext{mm}$$, what is the displacement current $$I_{disp}$$ between the plates?

Accepted Answer

$$1.74 	imes 10$$^{-5}$$ \ 	ext{A}$$

Question 2

Which of the following statements about electromagnetic waves is correct?

Accepted Answer

The electric and magnetic fields are perpendicular to each other and to the direction of wave propagation.

Question 3

The speed of light in glass is $$2.00 	imes 10^8$ \ 	ext{m/s}. $$What is the index of refraction of glass?

Accepted Answer

$$n = \frac{c}{v} = \frac{3.00 	imes 10^8$}{2.00 	imes 10^8$} = 1.50$$

Question 4

A Nd-YAG laser emits light with a wavelength of $$532 \ 	ext{nm} in $$vacuum. What is the frequency of this light?

Accepted Answer

$$f = \frac{c}{\lambda} = \frac{3.00 	imes 10^8$}{532 	imes 10$$^{-9}$$} = 5.64 	imes 10$$^{14}$$ \ 	ext{Hz}$$

Question 5

If the frequency of an electromagnetic wave remains constant but it enters water (where $$v_{water} = 2.25 	imes 10^8$ \ 	ext{m/s}$$), what happens to its wavelength compared to its value in vacuum?

Accepted Answer

The wavelength decreases.

Question 6

The intensity of sunlight reaching the Earth is $$1360 \ 	ext{W/m}^2. If $$the distance from the Sun to Mars is about $$1.52$$ times the distance from the Sun to Earth, what is the intensity of sunlight at Mars?

Accepted Answer

$$I_{mars} = I_{earth} \left( \frac{r_{earth}}{r_{mars}} \$$right)^2$$ = 1360 \left( \frac{1}{1.52} \$$right)^2$$ = 589 \ 	ext{W/m}^2$$

Question 7

If the amplitude of the electric field in an electromagnetic wave is doubled, what happens to the intensity of the wave?

Accepted Answer

The intensity increases by a factor of 4.

Question 8

A radio antenna emits electromagnetic waves with constant power and frequency. If you double your distance from the antenna, what happens to the amplitude of the electric field?

Accepted Answer

It becomes half its initial value.

Question 9

Which equation correctly relates the electric field amplitude $$E_0$$ and the magnetic field amplitude $$B_0 in an $$electromagnetic wave in vacuum?

Accepted Answer

$$E_0 = c$$ $$B_0$$

Question 10

A radio receiver can detect signals with electric field amplitudes as small as $$E_0 = 300$$ \ \mu	ext{V/m}$$. What is the smallest detectable intensity?

Accepted Answer

$$I = \frac{c \$$epsilon_0$$}{2} E_0$^2 = 1.19 	imes 10$$^{-10}$$ \ 	ext{W/m}^2$$

Question 11

Which of the following best describes the Poynting vector $$\vec{S}$$ for an electromagnetic wave?

Accepted Answer

$$\vec{S} = \frac{1}{\mu_0$} (\vec{E} 	imes \vec{B})$$, representing the energy flow per unit area per unit time.

Question 12

If an electromagnetic wave in vacuum has a magnetic field amplitude $$B_0 = 2.00$$ \ 	ext{mT}$$, what is the electric field amplitude E_0$?

Accepted Answer

$$E_0 = c$$ $$B_0 = 3.00$$ 	imes $$10^8$$ 	imes 2.00 	imes $$10^{-3} = 6.00$$ 	imes $$10^5$$ \ 	ext{V/m}$$

Question 13

Which of the following is true about the frequency of electromagnetic waves as they pass from vacuum into glass?

Accepted Answer

The frequency remains unchanged.

Question 14

A laser beam with power $$P is $$emitted isotropically. What is the intensity $$I at a $$distance $$r$$ from the source?

Accepted Answer

$$I = \frac{P}{4 \pi r^2$}$$

Question 15

Which of the following correctly describes the direction of propagation of an electromagnetic wave given $$\vec{E}$$ and $$\vec{B}$$?

Accepted Answer

The wave propagates in the direction of $$\vec{E} 	imes \vec{B}.$$

Question 16

If the intensity of an electromagnetic wave is $$10 \ 	ext{W/m}^2$$ and the electric field amplitude is doubled, what is the new intensity?

Accepted Answer

$$40 \ 	ext{W/m}^2$$

Question 17

Which of the following is the correct formula for the wavelength of light in a medium with index of refraction $$n_{medium}$$?

Accepted Answer

$$\lambda_{medium} = \frac{\lambda_{vacuum}}{n_{medium}}$$

Question 18

Which process involves the emission of a photon when an atom transitions from an excited state to a lower energy state without external influence?

Accepted Answer

Spontaneous emission

Question 19

A plane electromagnetic wave is coming toward you, out of the screen. At one instant, the electric field is directed to the right. What is the direction of the wave's magnetic field at this instant?

Accepted Answer

Up, according to the right hand rule

Electromagnetic Waves and Their Properties: Study Notes for Physics

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