MagneticFields

Magnetism

Interactions between magnets described in terms of poles.

“magnetic charges” – opposites attract

Interactions due to magnetic field .

Compass needles – align w/

Direction of force – direction of force on a N pole

Magnetic Field

Similar to :

• Vector field

• Two “charges” (poles)

Except…

No magnetic monopoles

Forces on Magnetic Charges

From empirical studies:

• toplane

Cross Products

Review Cross Products (Ch. 1)

CW: (i.e., )

CCW: (i.e., )

Forces on Magnetic Charges (cont.)

Direction (RHR):

• Point fingers of right hand in direction of

• Thumb: to fingers

• Curl fingers toward .

• Thumb points in direction of (on )

• : is opposite direction

Example

Determine the missing directions.

Direction of…

A

B

C

D particle 0

E C

F

Forces on Magnetic Charges (cont.)

Magnitude of the force

SI units: Teslas,

Another unit: Gauss,

In and :

Example

A charged particle travels with a speed of in a region where the magnetic field is in the direction and has a magnitude of . Determine the magnitude and direction of the magnetic force if the particle is (a) an electron traveling in the direction; (b) a proton traveling in the direction; (c) an particle traveling in the direction; and (d) an ion traveling in the direction.

Example

An electron travels in a straight line in the direction with a velocity of . There is both an electric and a magnetic field in this region. (a) If the magnetic field points in the direction and has a magnitude of , what is the magnitude and direction of the electric field? (b) A electric field points in the direction. What is the magnitude and direction of the magnetic field in this situation? The gravitational force on the electron can be ignored.

Magnetic Field Lines

Field lines can never intersect.

Field lines form closed loops (have no starting/ ending point).

Magnetic Field Lines (cont.)

Magnetic Flux

Units: , webers

Gauss’ Law for Magnetism:

Motion of Charged Particles in

does no work on a moving charge.

cannot change , only direction.

If , not :

Motion of Charged Particles in

does no work on a moving charge.

cannot change , only direction.

If , not :

Application: Velocity Selector

Charge moving in both and

with specific :

No deflection of particle (straight line).

Example

A negatively-charged chlorine isotope is accelerated through a potential difference of . It then enters a region of crossed electric and magnetic fields. (a) Which plate, or , has the higher potential? After exiting plate , the isotope then travels undeflected with speed through a region of crossed, uniform electric and magnetic fields. (b) Determine the charge-to-mass ratio of the isotope. (c) If , , , and , determine the mass of the isotope.

Application:

J. J. Thomson (for )

Accelerate through . Enter region w/ both and .

Conservation of energy + velocity selector.

Example

A charged isotope (charge , mass ) travels through a velocity selector undeflected with speed . It then enters a region where there is a magnetic field which has a magnitude of as shown in the figure. Determine, , the distance from where the isotope enters the second magnetic field the mass strikes the detector.

Application: Mass Spectrometer

Uses velocity selector to isolate isotopes

Radius of path (i.e., how far from opening strike detector)

All other values are measurable.

Magnetic Force on a Conductor

Conductor (length ) carries current in

Direction: same RHR for charges

: vector of length , in direction of

Magnitude:

Example

A loop of current is pulled into a region where there is a magnetic field as shown in the figure. If the length of the sides of the loop are , the current through the loop is and the magnetic field has a magnitude of , what is the net force on the loop?

Force on a Current Loop

Assume uniform .

Axis of rotation = axis.

Force & Torque on a Current Loop

due to , along axis.

due to due to

due to

Direction of : RHR (fingers = , thumb = )

Magnetic (Dipole) Moment

Direction of : RHR (fingers = , thumb = )

Points from S N

Potential Energy (& Coils)

Work to move through angle (align , ):

For stacked loops (i.e., a coil):

Example

The loop in the picture has a radius of and carries a current in the direction shown. The loop is free to rotate about an axis perpendicular to the page and is tilted so that a line perpendicular to the face of the loop makes an angle of with a magnetic field to the right. (a) Will this loop rotate clockwise or counterclockwise? (b) What is the magnitude of the torque on the loop?

Non-uniform

Axis of coil is parallel to page.

Looking toward magnet from right, is CW.

How to Magnetize An Object w/o Really Tryingor

Why Magnets “Stick” to the Fridge

S

N

N

S