Announcements 11/10/2018 E & M People Mechanics people Magnetostatics Exam Thursday Mechanics people 1996 FR exam check today 1995 FR exam due Friday If you missed the FR component to 1988 exam, you must take it today at lunch or tomorrow AMfor it to count as possible final. Otherwise, it is homework due Wednesday (turn in for correction)

Magnetic Fields Formed by moving charge Affect moving charge Units Tesla (SI) N/(Cm/s) N/(Am) Gauss 1 T = 104 gauss

Magnetic Dipole N S Magnetic Field (B)

Magnetic Forces CAN CANNOT accelerate charged particles by changing their direction cause charged particles to move in circular or helical paths CANNOT change the speed or kinetic energy of charged particles do work on charged particles

Magnetic Force on Charged Particle F = qv ✖ B magnitude: F = qvBsinθ q: charge in Coulombs v: speed in meters/second B: magnetic field in Tesla θ: angle between v and B

Magnetic Force on Current-carrying Wire F = iL ✖ B i: current in Amps L: length in meters (direction of current) B: magnetic field in Tesla

Torque on Wire Loop B a b i t = iabB F F t t

When v and B are at right angles to each other... qvBsinθ = mv2/r qB = mv/r q/m = v/(rB) B V F V F V F V F

Paths of charged particles in magnetic field Circle When velocity is perpendicular to field Helix When velocity has a component parallel to the field Straight When velocity is entirely parallel to field

Magnetic Force What can be concluded about the the charge of each particle? 1 3 2

Electric and Magnetic Fields Together B E q v = E/B

Beyond the 4th Grade N S B I

Ampere’s Law Used to calculate magnetic fields from current. The third of four Maxwell equations we’ve learned.

Ampere’s Law μoi = ∫ B•ds μo: magnetic permeability of free space (1.26 x 10-6 H/m) i: current (Amperes) B: magnetic field (Tesla) s: distance around Amperian loop (meters)

Ampere’s Law μoi = ∫ B•ds μoi = B2πR B = μoi/(2πR) i Amperian Loop of Radius R μoi = ∫ B•ds μoi = B2πR B = μoi/(2πR)

Ampere’s Law Can calculate magnetic fields inside and outside wires i

Ampere’s Law r B R R i0

Solenoid B = μoion

Amperes Law and Solenoids B = μoion μoi = ∫B·ds μoionL = BL

Ampere’s Law and Toroids Ampere’s Law tells us the magnetic field inside and outside the toroid is zero.

Ampere’s Law and Toroids μoNio = ∫B•ds B = μoNio/(2πr)

B = μoi1/(2πr) I1 I2 F = i2L ✖ B F = μoi1i2L/(2πr) What force does the magnetic field generated by i1 exert on i2? B = μoi1/(2πr)

In General… Parallel Currents Attract Antiparallel Currents Repel

What about the resulting magnetic field between wires?

Fields are weakened between parallel currents. I3 x B2 B3 B2 Fields are strengthened between anti-parallel currents.