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Maxwells Equations

- Electromagnetic

In the electric field E, and the magnetic field

B, a charge q will experience a force the

Lorentz force

F qE v B.

Static Charges produces E fields and Moving

charges produces B fields

Maxwells 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

Maxwells 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

solenoidal field, while one with a divergence but

no curl is called an irrotational field.

Electrostatic Field Potential Distribution.

Electrostatic Field

Equipotentials and Electric Field Vectors

of Electrostatic Field.

(No Transcript)

Electric Field Vectors

Equipotentials and Electric Field Vectors of

aMicrostrip Line.

Potential Distribution

Potential Distribution associated with a

Corner Resistor.

Electric Field Magnitude

Logarithmic scaled Electric Field Magnitude

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 eE

Where F is Force e is a charge, and E is electric

Field Intensity

Electrodynamics

- Newtons Second Law

d(mv)

dv

dm

F

m

v

dt

dt

dt

Where m mass of particle, kg V velocity of

particle, m-1

Electrodynamics

- Newtons Second Law
- F m

dv

ma

dt

ma eE

- Velocity is very small as compared to

velocity of light - Mass is essentially constant

Electrodynamics

- Energy

Integrating the force over the distance traveled

by charged particle is

2

2

W m ? a dL e? 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 eV

1

W ½ m( v22 v12) eV

Electrodynamics

- Particle Energy
- W eV 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 - e charge on particle, C
- m mass of particle, kg
- V magnitude of potential difference between

points 1 2, V

Electrodynamics

- Final velocity

Considering a charged particle e starting from

rest and passing through a potential of V, will

attain the final velocity of ?-

? ? 2eV/m

Electrodynamics

- Final velocity
- While
- e 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

Electrodynamics

eVd

eVdL

- ay

vy

vy ayt

? tan-1

vx

md

mvxd

L

Vd

y

v

vy

Ed

?

vx

d

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

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

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

Electrodynamics

- Magnetic Brake

Electrodynamics

- Magnetic Brake

I, B, PUSH Therefore F due to I is opposing to

PUSH

Conductive Plate

Magnet Assembly

Electrodynamics

- Magnetic Levitation

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.

How does the LEVITRON work?

- levitionta

Electrodynamics

- levitation

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

Electrodynamics

- Maglev Trains

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

Electrodynamics

- Maglev Train Track

Maglev Train

- Aerodynamics Brakes

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

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