Upload
or-ming-chun
View
79
Download
0
Embed Size (px)
Citation preview
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Some short notes on EM
Or Ming Chun
Apr 28th, 2011
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Table of contents1 Review on Electrostatic2 Electromagnetism
Magnetic field for different case3 Lorenz force law
Cross productLorenz force law
4 Magnetic Force and EM inductionExample : MotorInductionExample : Generator
5 SummaryM.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Electrostatic
E-field of charges is simply given by
E = q4πε0r2
Electric forced experienced by charges
F = qE
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Magnetic field for different case
Magnetic field for bar magnet
Figure: Magnetic field for a bar magnet
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Magnetic field for different case
Magnetic field for current carrying wire
Figure: Magnetic field for current carrying wire B = µ0I2πr
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Magnetic field for different case
Magnetic field for current carrying wire
Figure: Magnetic field for current carrying wire B = µ0I2πr
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Magnetic field for different case
Solenoid
Figure: Magnetic field for Solenoid B = µ0NIl
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Cross productLorenz force law
Cross product
Figure: Right Hand’srule for Cross product
2 vector a and b can becrossed to form newvector a × b
the direction of the newvector are shown in thefig.
|a × b| = |a||b| sin θ
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Cross productLorenz force law
Cross product
Figure: Directionof cross product
Here show the direction of thecross product
remember to use right hand!
Note that when 2 vector areparallel (θ = 0), the crossproduct are 0
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Cross productLorenz force law
Lorenz force law
How do charged particle move in Electromagneticfield?
Lorenz force law
F = q(E + v × B)
This consider both the effect of E-field andB-fieldThat’s why I introduce Cross productMost important : This concept can apply toboth left/right hand rule in the textbook tohelp you remember
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Example : MotorInductionExample : Generator
Magnetic Force
For a current carrying wire inside a B-field,
What is the Magnetic Force it experienced?
Current → moving of charge
Thus the direction of force experienced isF ∼ I × B
more explicit F = I × B = IB sin θ (per unitlength)
Magnetic force ∼ current × B-field
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Example : MotorInductionExample : Generator
Turning effect
Turning effect of coil in B-field can beincreased by:
1 increase the current2 increase the number of turns in the coil3 increase the area of the coil4 increase the strenght of the B-field
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Example : MotorInductionExample : Generator
Induction
so far we consider the Force on current wire byB-field, but to fill up the theory
Faraday’s Law
A changing Magnetic flux induce e.m.f
Lenz’s Law
Induced current oppose the change in
Magnetic flux
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Example : MotorInductionExample : Generator
Induction
Mathematically, Magnetic flux is given by:
Definition
Magnetic flux Φ = B · a = Ba cos θ
And Faraday’s Law and Lenz’s Law is :
Definition
Faraday’s Law −dΦdt = e.m.f.
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Example : MotorInductionExample : Generator
Direction of induced current
We can also find the direction of inducedcurrent by cross product
consider a wire moving in a region of B-field
v is the moving direction of the wire (charge)
then the charge will experience a force indirection F = v × B
this give the direction of the induced current
Thus, we have
Induced current ∼ motion × B-field
M.C. Or Some short notes on EM
Review on ElectrostaticElectromagnetism
Lorenz force lawMagnetic Force and EM induction
Summary
Direction of induced current
You have learnedmagnetic field line of typical itemsdirection and magnetiude of magnetic forceHow to remember Left/Right hand rule byusing only Lorenz force law, F = qv × BFaraday’s Law and Lenz’s LawOne final remark (Out syll but just want to tellyou more):
Changing B-field induce E-field ;Current or Changing E-field induce B-field
M.C. Or Some short notes on EM