Physics 1220/1320 Electromagnetism&Thermodynamics Lecture Magnetostatics, chapter 27-29

Magnetism - Contrary to common opinion, magnetism is just as common as electricity. -Magnetic fields are due to the motion of electric charges -All moving charges create magnetic fields -Electric and magnetic fields will turn out to be ‘coupled’ and the expression of the more general phenomenon of ‘electromagnetism’ -This phenomenon will explain the whole range of radiation and its ways of spreading. - Unlike electric charges, magnetism always comes in the form of two opposing poles (usually called North and South pole) -The magnetic force, magnetic field lines behave differently than the electric counterparts

Unlike poles attract, Like poles repel Unit ‘Tesla’ [T] = [N/(Am)], 10 k[G] = 1[T]

Many metals can be ‘magnetized’ when brought in contact with a magnet.

The molten material inside the earth rotates and creates a small magnetic field. Earth field near surface varies, ~ 1/3- 1/2 Gauss State of the art -Permanent magnets have field strength ~ 24[T] -Electromagnets up to Field strength which occur in nature: Sun 6[kG] pulsars 10^8 [T], magnetars [GT] b/w two atoms ~ up to 70 [T] … in technology: 50 ft from powerline 40[mG] 6’’ hair dryer 300[mG], microwave oven 6’’ 200[mG] 100[T]

Magnetic field B and magnetic force F B Unit ‘Tesla’ [T] = [N/(Am)], 10 k[G] = 1[T]

Magnetic Field Lines Magnetic flux  B, Gauss’s Law !

Mass Spectrometers: Magnetic fields can act as ‘velocity selectors’ for charged particles: v = E/B ie only particles with the right speed can pass through (condition:  F y =0) In the famous Thompson experiment, this effect was used to determine the ratio e/m for electrons. In the mass spectrometer, the effect is used to determine the mass of unknown particles with high precision.

Hall Effect Force on charge carrier in B  Transverse E builds through charge accumulation Due to F B until F E equal+opposite to F B  Hall voltage qE z +qv d B y =0 J x = nqv d nq= (-J x B y /E z )

Force on Current-Carrying Conductor

Force and Torque on a Loop Net force is zero Torque is zero if dA parallel B and max if perpendicular to B Magnetic dipole moment  =IA

Loops are important because electrons often perform loops, so material properties can be understood if one understands B for conductor loops. A potential energy is associated with the dipole moment in B. In B, coils will tend to turn toward their position of U min.

A case of practical importance is the energy of a coil in B: Consider a coil which rotates from an initial position into one where its  is parallel to B. Note:  = NIABsin 

How magnets work: Forces on current loops in non-uniform B dF = I dl x B Magnets in non-uniform fields – If free to move, all magnets will orient such that their axis // B

Permanent magnets: Random order Aligned atomic  ’s  tends to align  ’s with B Presence of B makes net  Non-uniform B  attractive force

Magnetic Field of moving charge Unit Tesla [T] = [(Ns)/(Cm)] = [N/(Am)]  [  0 ] = [N/A 2 ] = [Tm/A]‘permeability’ of free space and c 2 = 1/(  0  0 )

Forces between two moving electrons

Magnetic Field of a Current Element: Biot-Savart

B of Current Carrying Straight Conductor

Magnetic field of two wires

28.24 Find I 4 to make B at center of square zero:

Magnetic Field of a Circular Loop (atoms & electrons!)

Ampere’s Law

A more general integration path gives the same result, as long as the wire is included and the surface of integration is closed:

Field Inside a Long Cylindrical Conductor

Magnetic Field of a Solenoid