Lecture 20 Physics II Chapter 31

Electromagnetic Waves

Course website: http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Today we are going to discuss: Chapter 31:

 Section 31.5  31.6 (skip derivations of wave equations)  Section 31.7

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Displacement current/ Ampere-Maxwell Law Let’s get somehow an additional term with units of current and use it to generalize Ampere’s Law +Q –Q  ≝ E I=dQ/dt I d But we need something which has units of current. So let’s take a derivative:

Maxwell interpreted as being equivalent current and called it a Displacement current

∙ Ampere-Maxwell Law

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics  Displacement current E I I D I Displacement current 1) The displacement current is only between the plates since is zero outside

2) The way ID was introduced allows us to say that numerically ID=I (real current in the wire charging the capacitor). In some sense “current” is conserved all the way through the capacitor

3) ID is not a flow of charge. It is equivalent to a real current in that it creates the same magnetic field ∙ Let’s apply Ampere-Maxwell Law for the “capacitor system”

∙ ID Amperian Surface S1

∙ Amperian Surface S2 Now it works. Each surface gives us the same answer as it should be. PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Induced Magnetic Field

Ampere-Maxwell Law

∙

Thus, the magnetic field B can be generated by:

1) An ordinary electric current, Iin 2) Changing electric flux (particularly, changing electric field)

Another amazing thing!!!

Changing electric field inside a capacitor produces a magnetic field

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Induced Fields

. An increasing solenoid current causes an increasing magnetic field, which induces a circular electric field.

. An increasing capacitor charge causes an increasing electric field, which induces a circular magnetic field.

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics The last (4th) Maxwell’s equation

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Gauss’s Law for Magnetic Fields

Gauss’s law for the electric field says that for any closed surface enclosing total charge Qin, the net electric flux through the surface is:

There is a similar equation for a magnetic flux Magnetic field lines form continuous curves; every field line leaving a surface at some point must reenter it at another. Gauss’s law for the magnetic field states that the net magnetic flux through a closed surface is zero:

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Are We There Yet? Maxwell’s Equations

Electric and magnetic fields are described by the four Maxwell’s Equations: the physical meaning An electric field is produced by a charge

No magnetic monopoles

An electric field is produced by a changing magnetic field

A magnetic field is produced by a changing electric field or by a current In addition to Maxwell’s equations, which describes the fields, a fifth equation is needed to tell us how matter responds to these fields:

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics There are a total of 11 fundamental equations describing classical physics: 1. Newton’s first law

2. Newton’s second law Physics I 3. Newton’s third law 4. Newton’s law of gravity 5. Gauss’s law 6. Gauss’s law for magnetism Physics II 7. Faraday’s law 8. Ampère-Maxwell law 9. Lorentz force law

10. First law of thermodynamics Physics III 11. Second law of thermodynamics

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Electromagnetic Wave

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Light is an electromagnetic wave From Maxwell’s equations we can get wave equations for E and B: Traveling waves: y y y , Which can be solved: z , z z Angular Amplitude Wavenumber frequency According to the wave theory, this factor is v2 It travels  in +x direction ∙ The speed of light can be found 8 The magnitude of this speed is 3.0 x 10 m/s in two ways: – precisely equal to the measured speed of light. Thus, it means that light is an The oscillation amplitudes are related electromagnetic wave (shocking conclusion) Maxwell was the first to understand that light is an oscillation of the These propagating fields are called electromagnetic field. electromagnetic waves.

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Light is an electromagnetic wave (II)

The electric and magnetic waves are perpendicular to each other, and to the direction of propagation. Since a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field, they can propagate on their own.

Maxwell was able to predict that electromagnetic waves can exist at any frequency, not just at the frequencies of visible light.

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics ConcepTest Radio Antennas

If a radio transmitter has a vertical A) vertical antenna, should a receiver’s B) horizontal antenna be vertical or horizontal to obtain the best reception? C) doesn’t matter

If a wave is sent out from a vertical antenna, the electric field oscillates up and down. Thus, the receiver’s antenna should also be vertical so Vertical Horizontal that the arriving electric field can set antenna antenna the charges in motion. E field E field of wave of wave

Current Current is possible is impossible ConcepTest TV Antennas Before the days of cable, A) the circular one televisions often had two antennae on them, one straight B) the straight one and one circular. Which antenna C) both equally; they were picked up the magnetic straight and circular for oscillations? different reasons

The varying B field in the loop means the flux is changing and therefore an emf is induced. Polarization

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Polarization The plane of the electric field vector and the direction of propagation is called the plane of polarization.

The electric field in the figure oscillates The electric field in the figure above is vertically, so this wave is vertically horizontally polarized. polarized. Most natural sources of light are unpolarized, emitting waves whose electric fields oscillate randomly with all possible orientations.

Quantum cascade lasers emit vertically polarized light. PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Polarizers

The most common way of artificially generating polarized visible light is to send unpolarized light through a polarizing filter.

Polarizer axis

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Crossed polarizers

No Light Polarizer axis

Polarizer axis Two polarizing filters with perpendicular axes, called crossed polarizers, block all the light.

The polarizing direction of the first polarizer is oriented vertically to the incident beam so it will pass only the waves having vertical electric field vectors.

The wave passing through the first polarizer is subsequently blocked by the second polarizer, because this polarizer is oriented horizontally with respect to the electric field vector in the light wave.

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Polarizing Sunglasses

Wearing polarized sun glasses helps to reduce glare since vertically polarizing sunglasses can “cut glare” without affecting the main scene you wish to see. This horizontally polarized unwanted light is almost completely blocked by a vertical polarizing filter.

. Glare—the reflection of the sun and the skylight from roads, water and other horizontal surfaces—has a strong horizontal polarization.

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Thank you See you next time

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics Production of Electromagnetic Waves

Oscillating charges will produce electromagnetic waves:

2nd half cycle Far from the source, _ the waves are + _ plane waves + _ + Wave travel direction _ _ + _ + +

PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics