Magnetism: Force and Field

General Characteristics

• Like poles repel

• Unlike poles attract

• You can never isolate a north pole from a south pole. N

S

N

SN

S

N

S

Earth’s Magnetic Field

• North pole of compass is attracted to the north. Therefore, the north pole is a magnetic south pole.

• Measurements have indicated that the earth’s magnetic field is decreasing.

• There is evidence of pole reversal at the mid-Atlantic ridge.

N

S

Earth’s Magnetic Field

• Barnes noticed a 5% reduction in the earth’s magnetic field in 130 yrs.

• Reversing Magnetic Field recorded in the earth’s crust.

• Humphreys proposes rapid reversals due to the flood.

Unique Earth• Stable sun

• Nearly circular orbit

• Water present in 3 phases

• Magnetic field

• Ozone

• Nitrogen atmosphere

• Probability– 1069 to 1

Magnetic Force• Magnetic fields exert forces on moving

charges.

• Magnitude of the force is given by

• Direction of the force is determined by the right-hand rule.

• Units - Wb/m2 or T (1T = 104G)

BvqFB

sinqvBF

Force on a proton• Ex. What is the force on a proton traveling

60° with respect to a uniform magnetic field of 2.5 tesla at half the speed of light?

Only the perpendicularcomponent of the velocityproduces a magnetic force.

60sin)5.2)(/105.1)(106.1( 819 TsmCF

NF 11102.5

Will move in a helix.

Velocity Selector• Lorentz Force

• When F = 0 and

then

B

EBvqEqF

BEv

B

Ev

p+

Mass Spectrometer

• When the velocity is known, then the mass is known by the charge and radius of curvature in a B field.

p+

E B

qB

mvr

Motion in a Magnetic Field

• component of velocity will cause circular motion.

rqvBFr

vm

2

qB

mvr

Cyclotron Frequency

m

qB

r

v

v

B

Cyclotron• 2 sets of D magnets are set up

to bend charged particles into a circular path.

• An alternating electric field between the D magnets causes the particles to speed up.

• The particles spiral outward with increasing speed.

B

E

p+

Force on a Wire• In a uniform magnetic field a straight wire

experiences a force.

• In general for all wires in magnetic fields

• For a uniform magnetic field only the displacement from the starting point to the ending point affects the magnetic force.

BlIF

BsdIFd

Force on a Loop• Ex. What is the force on a

semicircle shaped loop, if the straight portion has a force of 8 N on it?

• What is the current in the loop if the radius of curvature is 0.75m and the magnetic field is 2 T?

Torque on a Loop• Remember

• For a uniform field to the current

• then for a force arm

to the magnetic force

Fr

BsdIFb

a

BlIF

AIBIBalaIlB )2(2

BAI

2a

F

F

B

Torque on a Dipole

• Remember

• then

Fr

Erq

EqF

2aq

q+

F

F

E

Moments• Magnetic Moment

• Electric Dipole Moment

AI

B

raqp ˆ 2

Ep

r̂ is a unit vector going from thenegative to the positive charge

Electric Energy

• Ex. What is the torque on a circular loop with radius of 5 cm rotating at 0.25 Hz if it has a current of 1A and is in a uniform magnetic field of 0.2 T?

N SS N NS

Coil Rotates

Biot-Savart Law• Magnetic fields are generated by moving

charge.

2

ˆ

r

rsIdkBd m

mAWbkm /104

70

0 - permeability of free space

I

r̂

r

ds

B Field for a Wire• For a thin straight conductor carrying

current the magnetic field is

• Use the right hand rule to determine the direction. (Place thumb in direction of current and B Field is in direction of fingers grabbing the wire.)

• Effect of moving charges is transmitted at the speed of light. Magnetism is the result of moving charges.

a

IB

2

0

Ia

Attraction of Wires

• Magnetic Force of one wire interacts with the current in the other wire.

• This concept is used to define the Ampere and the Coulomb.

• Find the attraction between two wires carrying 10 A each that are 1 mm apart?

a

IIllBIF

2

210211

Ampere’s Law• The line integral of B·ds around any closed

path equals 0I, where I is the total steady current flowing through the surface bounded by the closed path.

IsdB 0I

a

B field for a Wire• Chose a closed loop which follows the

magnetic field, which is constant in value.

• Therefore,

• This matches our result from using Biot-Savart Law.

rBdsBsdB 2

IrB 02 r

IB

2

0

Ir

ds

B field for a Toroid

• A toroid is a donut shape with a coil wrapped around it.

• Therefore,

• Get a concentrated field inside the toroid.

ds

rNIrBsdB 02

r

NIB

20

B field in a Solenoid

• A long wire is wound in the form of a helix.

• Let a solenoid consist of N turns over a distance of l.

dsl

NIBlsdB 0

nIl

NIB 0

0

Gauss’ Law• Magnetic Flux - Amount of magnetic field

leaving a surface.

• Since magnetic field lines form loops you can never find an isolated magnetic pole.

AdBm

0

surfaceclosed

AdB

Magnetism• Sources

– Orbital magnetic moment of an electron.– Spin magnetic moment of an electron.

• Types of Magnetism– Ferromagnetic– Paramagnetic– Diamagnetic

Ferromagnetism• Consists of small regions

(called domains) where the magnetic moments are aligned.

• Using an external magnetic field you can align the domains.

Hysteresis• A remnant magnetic field

remains when an external field is removed.

• To remove a magnetic field a oscillating magnetic field with decreasing amplitude needs to be used.

Bapplied

Binternal

Magnetic Recording

• Iron embedded on a surface can store direction of a magnetic field.

Paramagnetism• Weak interaction between magnetic

moments within the material.

• Magnetic moments will align in the presence of an external magnetic field.

• If the material is lowered below the Curie temperature, it will maintain its magnetic alignment.

Diamagnetism• Has no permanent magnetic moment.

• The presence of an external magnetic field causes a weak opposing magnetic moment in the material.

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