PHYSICS - KNIGHT CALC 4E CH 31: ELECTROMAGNETIC FIELDS...

! www.clutchprep.com

!

PHYSICS - KNIGHT CALC 4E

CH 31: ELECTROMAGNETIC FIELDS AND WAVES

CONCEPT: WHAT IS AN ELECTROMAGNETIC WAVE? ● An electromagnetic wave is a wave composed of oscillating ___________________ and ___________________ fields.

EXAMPLE: Blue light with a wavelength of 450 nm travels through a medium where 𝜖 = 4𝜖0, but 𝜇 = 𝜇0. What is the

speed of the blue light in this medium?

● Electromagnetic waves carry the following properties:

- They are [ LONGITUDINAL / TRANSVERSE ] waves

- The speed of light defines the ratio of the electric and magnetic fields, 𝐸 = ___________

- Electromagnetic waves [ DO / DO NOT ] need a medium to propagate.

● The SPEED OF LIGHT in a vacuum is a constant:

𝑐 =1

√𝜖0𝜇0= ________________________



PRACTICE: DISTANCE TO MARS

If a lightyear is defined as the distance light travels in one year, what do you think a lightminute is? If Mars is 12 lightminutes

away, how far away is it in meters? How long would it take to send a radio transmission to Mars?



CONCEPT: THE ELECTROMAGNETIC SPECTRUM ● Light of different energy has dramatically different properties

- The ELECTROMAGNETIC SPECTRUM is an arrangement of light based on its energy content

- The energy of light is proportional to the frequency of the light, and inversely proportional to the wavelength

● RADIO waves are used to transmit information over long distances, and are used in radios ● MICROWAVES happen to have just the right amount of energy to vibrate water molecules, which allow them to heat food ● The VISIBLE LIGHT spectrum is the portion of the electromagnetic spectrum we can see

- The visible light spectrum typically follows the acronym ROYGBIV from lowest to highest energy

- White light is formed by a combination of multiple colors ● X-RAYS are the first type of ionizing radiation: the kind of radiation that does real damage to living organisms

- Low energy X-rays are used in medical imaging, with X-ray images and CT scans ● GAMMA-RAYS are the highest energy form of electromagnetic radiation and are extremely hazardous to living organisms

- Gamma-rays are the cause of most of the damage from nuclear weapons or nuclear plant meltdowns

EXAMPLE: Which is more energetic, long wave radio waves or short wave radio waves?



CONCEPT: ENERGY CARRIED BY ELECTROMAGNETIC WAVES ● There are two types of energy carried by electromagnetic waves: ___________________ and ___________________

● It is also useful to define the power carried per unit area by a wave - This is sometimes referred to as the POYNTING FLUX ● The INTENSITY of the wave is just the average of the Poynting flux EXAMPLE: A laser outputs light at an average of 0.5 nW. If the light is emitted from the laser in a cylindrical beam of radius

0.5 mm, what is the intensity of the light? What is the maximum value of the electric field?

● The electric and magnetic ENERGY DENSITY carried by an electromagnetic wave is

𝑢𝐸 = _______________ 𝑢𝐵 = _______________ ● So, the TOTAL ENERGY DENSITY carried by an electromagnetic wave is

𝑢 = ______________________________ = _______________

𝑺 = 𝒄𝒖 = 𝒄𝝐𝟎𝑬𝟐

𝑰 = 𝑺𝒂𝒗 =𝟏

𝟐𝝐𝟎𝒄𝑬𝒎𝒂𝒙

𝟐



PRACTICE: ELECTRIC AND MAGNETIC FIELD EMITTED BY A LIGHTBULB A 100 W lightbulb actually emits around only 10 W of light. What is the intensity of the light 1 cm away if the light is emitted perfectly spherically? What is the magnitude of the electric field emitted by the lightbulb? What about the magnetic field?



CONCEPT: ELECTROMAGNETIC WAVES AS SINUSOIDAL WAVES ● As we known, a common electromagnetic wave is sinusoidal

- The �⃗� pointing in the x-direction

- The �⃗� pointing in the y-direction

- Propagation in the z-direction

EXAMPLE: The following are the electric and magnetic fields that describe a particular electromagnetic wave. What is the

wavelength of this wave? The period?

�⃗� = (1 × 105 𝑁

𝐶) sin[(1.4 × 107𝑚−1)𝑥 − (4.19 × 1015𝑠−1)𝑡]

�⃗� = (3.33 × 10−4 𝑇) sin[(1.4 × 107𝑚−1)𝑥 − (4.19 × 1015𝑠−1)𝑡]

● Because of this, it is easy to describe the electric and magnetic fields, separately, as sine functions

�⃗⃗� = ____________________________ �⃗⃗� = ____________________________



CONCEPT: POLARIZATION FILTERS ● The POLARIZATION of an electromagnetic wave is the angle of the _____________________, relative to some 0o angle.

● When unpolarized light passes through a polarizing filter, the intensity drops by HALF

EXAMPLE: Unpolarized light passes through a polarization filter with an angle of 45o relative to the vertical. This newly

polarized light passes through a second polarization filter, with an angle of 55o relative to the vertical. If the intensity of the

unpolarized light was 100 W/m2, what’s the intensity of the light after passing through the second polarization filter?

● Whenever initialized POLARIZED light passes through a polarizer, the intensity drops:

𝐼 = _______________________

𝑰 =𝟏

𝟐𝑰𝟎



EXAMPLE: INITIALLY VERTICALLY POLARIZED LIGHT Initially vertically polarized light carries an intensity of 0.55 W/m2. If you had an adjustable polarizer, what angle to the

vertical would you want to align it so that the intensity of the light exiting the polarizer would be 0.2 W/m2?

PRACTICE: THREE DIFFERENT POLARIZING SCENARIOS In each of the following cases, initially vertically polarized light enters the polarizing apparatus with the same initial intensity. Which polarizing apparatuses will cause the light to exit with the largest intensity, 90o from its initial polarization? a) A single polarizing filter, oriented 90o from the vertical b) Two polarizing filters, the first 45o from the vertical and the second 90o from the vertical c) Two polarizing filters, the first 60o from the vertical and the second 90o from the vertical d) Two polarizing filters, the first 30o from the vertical and the second 90o from the vertical.



CONCEPT: DISPLACEMENT CURRENT AND MAXWELL’S EQUATIONS

● Currently, Ampere’s law looks like ∫ �⃗� ⋅ 𝑑𝑙 = 𝜇0𝑖𝐶 ● There is actually a second “current” that can produce a magnetic field, according to Ampere’s law - This second “current” is known as the displacement current

EXAMPLE: What is the magnetic field produced between the two capacitor plates shown below?

● After correcting for the displacement current, MAXWELL’S EQUATIONS become - Gauss’ Law for Electric Fields - Gauss’ Law for Magnetic Fields - Faraday’s Law - Ampere’s Law

● The DISPLACEMENT CURRENT is given by

𝑖𝐷 = ______________________

𝑖𝑐 𝑖𝑐

�⃗�

𝑅

𝑟

∮ �⃗⃗� ⋅ 𝒅�⃗⃗� =𝒒𝒆𝒏𝒄

𝝐𝟎

∮ �⃗⃗� ⋅ 𝒅�⃗⃗� = 𝟎

∮ �⃗⃗� ⋅ 𝒅𝒍 = −𝒅𝚽𝑩

𝒅𝒕

∮ �⃗⃗� ⋅ 𝒅𝒍 = 𝝁𝟎 (𝒊𝒄 + 𝝐𝟎

𝒅𝚽𝑬

𝒅𝒕)



PHYSICS - KNIGHT CALC 4E CH 31: ELECTROMAGNETIC FIELDS...

Documents

Transcript of PHYSICS - KNIGHT CALC 4E CH 31: ELECTROMAGNETIC FIELDS...