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16.360 Lecture 21 Today • Magnetic forces and Torques • The Biot-Savart Law • Magnetic force between two parallel conductors • Maxwell’s magnetic potential

16.360 Lecture 21 Today Magnetic forces and Torques The Biot-Savart Law Magnetic force between two parallel conductors Maxwell’s magnetic potential

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Page 1: 16.360 Lecture 21 Today Magnetic forces and Torques The Biot-Savart Law Magnetic force between two parallel conductors Maxwell’s magnetic potential

16.360 Lecture 21

Today

• Magnetic forces and Torques• The Biot-Savart Law• Magnetic force between two parallel conductors• Maxwell’s magnetic potential

Page 2: 16.360 Lecture 21 Today Magnetic forces and Torques The Biot-Savart Law Magnetic force between two parallel conductors Maxwell’s magnetic potential

16.360 Lecture 21

Magnetic forces and Torques

,0 B

,JH

Magnetostatics

,HB

,0 r

,BuqFm

,BuqEqFFF me

Page 3: 16.360 Lecture 21 Today Magnetic forces and Torques The Biot-Savart Law Magnetic force between two parallel conductors Maxwell’s magnetic potential

16.360 Lecture 21

Magnetic forces on a current-carrying conductor

,BlIddFm

),( BldIFCm

x

x x x x

x

xxx

x x x

I

Page 4: 16.360 Lecture 21 Today Magnetic forces and Torques The Biot-Savart Law Magnetic force between two parallel conductors Maxwell’s magnetic potential

16.360 Lecture 21

Magnetic torques on a current-carrying conductor

,FdT

,ˆ)ˆ()ˆ( 001 IbBzBxbyIF

,ˆ)ˆ()ˆ( 003 IbBzBxbyIF

,ˆˆ)ˆ()2

ˆ(

)ˆ()2

ˆ(

000

03311

IAByIabByIbBzax

IbBzaxFdFdT

Page 5: 16.360 Lecture 21 Today Magnetic forces and Torques The Biot-Savart Law Magnetic force between two parallel conductors Maxwell’s magnetic potential

16.360 Lecture 21

The Biot-Savart Law

4 2R

RldIHd

4 2

l R

RldIH

.

R̂ld

2R

H

Magnetic force between two parallel conductor

,2

ˆ 101 d

IxB

,2

ˆ

2)ˆ(ˆˆ

210

102122

d

lIIy

d

IxzlIBzlIF

Page 6: 16.360 Lecture 21 Today Magnetic forces and Torques The Biot-Savart Law Magnetic force between two parallel conductors Maxwell’s magnetic potential

16.360 Lecture 21

Gauss’s Law for Magnetism

,vD

Ampere’s Law

,vSQsdD

,0 B

,vSQsdB

,JH

,)( IsdJsdHSS

,IsdJldHSC