ElectromagnetElectromagnet

Wire FieldWire Field A moving charge generates a A moving charge generates a

magnetic field.magnetic field.• Symmetry with experiencing Symmetry with experiencing

forceforce

• Perpendicular to direction of Perpendicular to direction of motionmotion

• Circles around pathCircles around path

Outside a straight wire the Outside a straight wire the magnetic field is cylindrical.magnetic field is cylindrical.• Decreases inversely with Decreases inversely with

distancedistance

I

B

r

IB

2

PermeabilityPermeability

The permeability The permeability defines the strength of the B field in a defines the strength of the B field in a material.material.

The vacuum permeability is The vacuum permeability is 00..

• Defined as Defined as 00 = 4 = 4 x 10 x 10-7-7 T m / A T m / A

The permeability is constant for most materials.The permeability is constant for most materials.• Usually close to Usually close to 00

• Not constant for ferromagnetic materials like iron Not constant for ferromagnetic materials like iron >> 00

Mutual AttractionMutual Attraction Two parallel wires with current Two parallel wires with current

will exert a force on each will exert a force on each other.other.• Wire length Wire length ll

• Separation Separation dd

Currents in the same direction Currents in the same direction attract.attract.

Currents in the opposite Currents in the opposite direction repel.direction repel.

d

IB

2

1012

I1

dI2

d

lIIlBIF

2210

12212

l

Wire ForceWire Force Find the force per unit length Find the force per unit length

experienced by each of two experienced by each of two long parallel wires in avacuum long parallel wires in avacuum separated by 1.0 m carrying separated by 1.0 m carrying currents of 1.0 A.currents of 1.0 A.

This is the official definition of This is the official definition of the SI unit of the ampere (A).the SI unit of the ampere (A).• 1 A = 1 C/s1 A = 1 C/s

Convert the force on the wire Convert the force on the wire into a force per unit length.into a force per unit length.

• F/lF/l = (4 = (4 x 10 x 10-7-7 Tm/A)(1.0 A)2 / Tm/A)(1.0 A)2 / 22 (1.0 m) (1.0 m)

• F/l F/l = 2 x 10= 2 x 10-7-7 N/m N/m

d

II

l

F

2

21012

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length.

Loop FieldLoop Field Each segment of a loop of Each segment of a loop of

current contributes a circular current contributes a circular field.field.• All the same direction inside All the same direction inside

looploop

• Similar to a dipole patternSimilar to a dipole pattern

Field strength depends on Field strength depends on radius of loop radius of loop RR..

R

IB

2

SolenoidSolenoid

Multiple parallel loops form a solenoid.Multiple parallel loops form a solenoid.• Each of N loops contributes a share of the fieldEach of N loops contributes a share of the field• Solenoids create very uniform magnetic fields Solenoids create very uniform magnetic fields

R

INB

2

Tight, short coil

Close LoopsClose Loops Field in a solenoid varies at the Field in a solenoid varies at the

edges from each loop of wire.edges from each loop of wire.

Closer loops in a solenoid Closer loops in a solenoid make a stronger field.make a stronger field.• Turns per length Turns per length n = N/ln = N/l

• Formula changes for a long Formula changes for a long coilcoil

A split coil would have half the A split coil would have half the field.field.• Equivalent to saying half the Equivalent to saying half the

field leaks out between loops.field leaks out between loops.

B

NI

l

nIB

ElectromagnetElectromagnet

next

An electromagnet is usually a An electromagnet is usually a solenoidal coil of wire.solenoidal coil of wire.

Increasing the permeability will Increasing the permeability will increase the field lines.increase the field lines.• Iron core solenoidIron core solenoid