Maxwell s equations
Download
1 / 32

- PowerPoint PPT Presentation


  • 68 Views
  • Uploaded on

Maxwell’s Equations. In the electric field E, and the magnetic field B , a charge q will experience a force: the Lorentz force:. Electromagnetic. F = q{E + v × B}. Static Charges produces E fields and Moving charges produces B fields. Maxwell’s Equations. Electromagnetic.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about '' - aphrodite-stathos


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Maxwell s equations

Maxwell’s Equations

In the electric field E, and the magnetic field B, a charge qwill experience a force: the Lorentz force:

Electromagnetic

F = q{E + v × B}.

Static Charges produces E fields and Moving charges produces B fields


Maxwell s equations1
Maxwell’s Equations

Electromagnetic

The effects may be summarized in the expressions for the divergence and the curl of E and B:

divE = /,

curlE = 0 ,

divB = 0 ,

curlB = µ0J


Maxwell s equations2
Maxwell’s Equations

Electromagnetic

Equations without divergence and curl express passive aspects, while with curl and divergence express active aspects.

A field with a curl but no divergence is

called a solenoidalfield, while one with a divergence but no curl is called an irrotationalfield.



Electrostatic field
Electrostatic Field

Equipotentials and Electric Field Vectors of

Electrostatic Field.


Electric field vectors
Electric Field Vectors

Equipotentials and Electric Field Vectors of aMicrostrip Line.


Potential distribution
Potential Distribution

Potential Distribution associated with a Corner

Resistor.


Electric field magnitude
Electric Field Magnitude

Logarithmic scaled Electric Field Magnitude


Electrodynamics
Electrodynamics

A Charged Particle

If a charged particle is set free in an electric field, it is accelerated by a force proportional to the field and charged particle

F = qE

Where F is Force

q is a charge, and

E is electric Field Intensity


Electrodynamics1
Electrodynamics

Newton’s Second Law

d(mv)

dv

dm

F =

= m

+ v

dt

dt

dt

Where m = mass of particle, kg

V = velocity of particle, m-1


Electrodynamics2
Electrodynamics

Newton’s Second Law

F = m

dv

= ma

dt

ma = qE

  • Velocity is very small as compared to velocity of light

  • Mass is essentially constant


Electrodynamics3
Electrodynamics

Energy

Integrating the force over the distance traveled by charged particle is

2

2

W = m  a •dL = q E • dL

1

1

While the Integral of E between points of 1 and 2 is a potential difference V

2

W = m v •dv = qV

1

W = ½ m( v22 – v12) = qV


Electrodynamics4
Electrodynamics

Particle Energy

W = qV = ½ mv2

where

W = energy acquired by particle, J

v2 = velocity of particle at point 2, or final velocity, ms-1

V1 = velocity of particle at point 1, or initial velocity, ms-1

q = charge on particle, C

m = mass of particle, kg

V = magnitude of potential difference between points 1 & 2, V


Electrodynamics5
Electrodynamics

Final velocity

Considering a charged particle q starting from rest and passing through a potential of V, willattain the final velocity of :-

 =  2qV/m


Electrodynamics6
Electrodynamics

Final velocity

While

q = 1.6 x 10-19C falling through

V = 1 volt

Energy = 1.6 x 10-19 Joules

m = mass of 0.91 x 10-30kg, will attain Velocity = v = 5.9 x 105 V

at 1 volt the charge attains 590 kms-1


Electrodynamics7
Electrodynamics

ay =

qVd

qVdL

vy

; vy = ayt =

;  = tan-1

vx

md

mvxd

L

Vd

y

vy

v

Ed

vx

d


Electrodynamics8
Electrodynamics

Problem:-

A CRT with Va = 1500V,

Deflecting space d = 10mm,

Deflecting plate length = 10mm,

Distance x = 300mm,

Find Vd to deflection of 10mm:-

Deflection y = VdLx/2Vad

Vd = 2Vady/Lx= 100 V


Electrodynamics9
Electrodynamics

Moving particle in static magnetic field

Force on a current element dL in a magnetic field is given by:

dF = (I x B)dL (N) …Motor equation

I = q/t

IL = qL/t = qv

IdL = dqv

dF = dq(v x B)

F = e(v x B) Lorentz force


Electrodynamics10
Electrodynamics

Moving conductor in a magnetic field

E = F/e = v x B

V12 =  E • dL =  (v x B) • dL

2

2

1

1

1

Generating Equation

B

dL

v

2

E = v x B


Electrodynamics11
Electrodynamics

Magnetic Brake


Electrodynamics12
Electrodynamics

Magnetic Brake

I, B, & PUSH

Therefore F due to I is opposing to PUSH

Conductive Plate

Magnet Assembly


Electrodynamics13
Electrodynamics

Magnetic Levitation


How does the levitron work
How does the LEVITRON¨ work?

When the top is spinning, the torque acts gyroscopically and the axis does not overturn but rotates about the (nearly vertical) direction of the magnetic field.



Electrodynamics14
Electrodynamics

levitation


Electrodynamics15
Electrodynamics

levitation

"We may perhaps learn to deprive large masses of their gravity and give them absolute levity, for the sake of easy transport."

- Benjamin Franklin


Electrodynamics16
Electrodynamics

Maglev Trains


Electrodynamics17
Electrodynamics

Maglev Train

A maglev train floats about 10mm above the guidway on a magnetic field. It is propelled by the guidway itself rather than an onboard engine by changing magnetic fields (see right). Once the train is pulled into the next section the magnetism switches so that the train is pulled on again. The Electro-magnets run the length of the guideway


Electrodynamics18
Electrodynamics

Maglev Train Track


Maglev train
Maglev Train

Aerodynamics Brakes


Electrodynamics19
Electrodynamics

Advantages:

  • no components that would wear out

  • there is no friction. Note that there will still be air resistance.

  • less noise

  • The final advantage is speed