1 / 40

410 likes | 675 Views

E produced by changing B. How about outside ro ?. Problems with Ampere's Law. But what if

Download Presentation
## general form of faraday s law

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**1: **General form of Faraday’s Law

**3: **Problems with Ampere’s Law

**4: **But what if…..

**5: **Maxwell’s correction to Ampere’s Law

**6: **Maxwell’s Equations

**7: **Gauss’s law (electrical):
The total electric flux through any closed surface equals the net charge inside that surface divided by eo
This relates an electric field to the charge distribution that creates it
Gauss’s law (magnetism):
The total magnetic flux through any closed surface is zero
This says the number of field lines that enter a closed volume must equal the number that leave that volume
This implies the magnetic field lines cannot begin or end at any point
Isolated magnetic monopoles have not been observed in nature

**8: **Faraday’s law of Induction:
This describes the creation of an electric field by a changing magnetic flux
The law states that the emf, which is the line integral of the electric field around any closed path, equals the rate of change of the magnetic flux through any surface bounded by that path
One consequence is the current induced in a conducting loop placed in a time-varying B
The Ampere-Maxwell law is a generalization of Ampere’s law
It describes the creation of a magnetic field by an electric field and electric currents
The line integral of the magnetic field around any closed path is the given sum

**9: **The Lorentz Force Law Once the electric and magnetic fields are known at some point in space, the force acting on a particle of charge q can be calculated
F = qE + qv x B
This relationship is called the Lorentz force law
Maxwell’s equations, together with this force law, completely describe all classical electromagnetic interactions

**10: **Maxwell’s Equation’s in integral form dS = n dA
Flux = field integrated over a surface
No magnetiic monopoles
E .dl is an EMF (volts)dS = n dA
Flux = field integrated over a surface
No magnetiic monopoles
E .dl is an EMF (volts)

**11: **Maxwell’s Equation’s in free space (no charge or current) dS = n dA
Flux = field integrated over a surface
No magnetiic monopoles
E .dl is an EMF (volts)dS = n dA
Flux = field integrated over a surface
No magnetiic monopoles
E .dl is an EMF (volts)

**12: **Hertz’s Experiment An induction coil is connected to a transmitter
The transmitter consists of two spherical electrodes separated by a narrow gap
The discharge between the electrodes exhibits an oscillatory behavior at a very high frequency
Sparks were induced across the gap of the receiving electrodes when the frequency of the receiver was adjusted to match that of the transmitter
In a series of other experiments, Hertz also showed that the radiation generated by this equipment exhibited wave properties
Interference, diffraction, reflection, refraction and polarization
He also measured the speed of the radiation

**13: **Implication A magnetic field will be produced in empty space if there is a changing electric field. (correction to Ampere)
This magnetic field will be changing. (originally there was none!)
The changing magnetic field will produce an electric field. (Faraday)
This changes the electric field.
This produces a new magnetic field.
This is a change in the magnetic field.

**14: **An antenna

**15: **Look at the cross section

**16: **Angular Dependence of Intensity This shows the angular dependence of the radiation intensity produced by a dipole antenna
The intensity and power radiated are a maximum in a plane that is perpendicular to the antenna and passing through its midpoint
The intensity varies as
(sin2 ?) / r2

**18: **Harmonic Plane Waves

**19: **Applying Faraday to radiation

**20: **Applying Ampere to radiation

**21: **Fields are functions of both position (x) and time (t)

**22: **The Trial Solution The simplest solution to the partial differential equations is a sinusoidal wave:
E = Emax cos (kx – ?t)
B = Bmax cos (kx – ?t)
The angular wave number is k = 2p/?
? is the wavelength
The angular frequency is ? = 2pƒ
ƒ is the wave frequency

**23: **The trial solution

**24: **The speed of light (or any other electromagnetic radiation)

**26: **The electromagnetic spectrum

**28: **Another look

**29: **Energy in Waves

**30: **Poynting Vector Poynting vector points in the direction the wave moves
Poynting vector gives the energy passing through a unit area in 1 sec.
Units are Watts/m2

**31: **Intensity The wave intensity, I, is the time average of S (the Poynting vector) over one or more cycles
When the average is taken, the time average of cos2(kx - ?t) = ½ is involved

**33: **Radiation Pressure

**34: **Pressure and Momentum For a perfectly reflecting surface,
p = 2U/c and P = 2S/c
For a surface with a reflectivity somewhere between a perfect reflector and a perfect absorber, the momentum delivered to the surface will be somewhere in between U/c and 2U/c
For direct sunlight, the radiation pressure is about 5 x 10-6 N/m2

**36: **Background for the superior mathematics student!

**37: **Harmonic Plane Waves

**38: **Phase Velocity - Another View

**39: **Vector Calculus Theorems

**40: **Maxwell’s Equation’s In Differential Form

More Related