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Current - Electricity and Optics - Lecture Slides, Slides of Electrical Engineering

You can find here lecture series for complete Electricity and Optics course. All related topics are explained in slides. This lecture slides contain: Current , Gauss’ Law, Ampere's Law, Gauss’ Law for Magnetism, Solenoid, Dipole Moments, Bound Current, Magnetization, Magnetic Susceptibility, Diamagnetic

Typology: Slides

2012/2013

Uploaded on 08/20/2013

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LECTURE 15
Force between Current Carrying Wires
Gauss’ Law for Magnetism
Ampere’s Law
Magnetism in Matter
Force between Two Parallel Current Carrying
Wires
*Parallel currents attract
*Anti-parallel currents repel
F
=I L
×B
Force between Two Parallel Current Carrying
Wires
2/27/12 4
13.5 V I1 I2 ,
depending
on switch
position
A500~II 21 +
parallel
wires
R1 R2
DEMO
pf3
pf4
pf5

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LECTURE 15

  • Force between Current Carrying Wires
  • Gauss’ Law for Magnetism
  • Ampere’s Law
  • Magnetism in Matter

Force between Two Parallel Current Carrying

Wires

*Parallel currents attract *Anti-parallel currents repel F  = I L  × B 

Force between Two Parallel Current Carrying

Wires

2/27/12 4 13.5 V

I 1 I 2 ,

depending

on switch

position

I 1 + I 2 ~ 500 A

parallel

wires

R 1 R 2

DEMO

2/27/12 5

I 1 I

I 2 1 I 2

attraction repulsion

Collapse or expansion?

Force Between two Parallel Current Carrying

Wires

2/27/12 6

Gauss’ Law for Magnetism

Since all lines of B are closed loops, any B line leaving a closed surface MUST reenter it somewhere. TRUE IN GENERAL, not just for this “dipole” example

Φ Bnet =

B i d

∫^ A^ =^0

2/27/12 7

Compare Gauss’ Law for Electric Fields

Φ Enet =

E i d

A =

Qenclosed

ε o

  • Calculate field at distance r from wire using Ampere's Law:

Ampere’s Law

B i d

∫^ l^ =^ μ o^ IEnclosed

B dl = 0 2 π r

∫^ μ o^ I

2 π rB = μ o I B = μ o I 2 π r

2/27/12 13

Force between a Solenoid & a Current Carrying

Wire (DEMO)

2/27/12 14

Magnetic Field Inside a Toroid

2/27/12 15

When Ampere’s Law doesn’t Help

current is not continuous B can’t be factored out of the integral. insufficient symmetry finite length current segment

Dipole Moments in Applied Fields

2/27/12 16

Magnetization and “Bound Current”

2/27/12 17 Net current inside the material is zero. We are left with a surface current and therefore a magnetic moment

Magnetization and “Bound Current”

2/27/12 18 2/27/12 19

Magnetization and Magnetic Susceptibility

2/27/12 20

Magnetic Materials fall into Three Categories

Category m Km Paramagnetism *increase in B is small *aligns with Bapp Order of (+10–5), depends on temperature

Diamagnetism Decrease in B is small aligns opposite Bapp Order of (–10–5) 1 – # Ferromagnetism High degree of alignment even in weak Bapp positive and large ~ m