Some short notes on EM

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



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



Summary

Electrostatic

E-field of charges is simply given by

E = q4πε0r2

Electric forced experienced by charges

F = qE




Summary

Magnetic field for different case

Magnetic field for bar magnet

Figure: Magnetic field for a bar magnet




Summary


Magnetic field for current carrying wire

Figure: Magnetic field for current carrying wire B = µ0I2πr




Summary


Solenoid

Figure: Magnetic field for Solenoid B = µ0NIl




Summary


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




Summary


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




Summary


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




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




Summary


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




Summary


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




Summary


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.




Summary


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




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


Some short notes on EM

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