Magnetic Force On a moving charge §21.2

Vector Direction Conventions Right Left Up Down In Out

Magnetic Force on a Charge F = qv  B Source: Griffith, The Physics of Everyday Phenomena F is directed out of the screen.

Vector Cross Product Operation symbol  Another way to multiply two vectors Product is a vector! Direction of AB is perpendicular to both A and B

Cross Product Magnitude A  B = ab sin q A q Maximum for q = 90° Zero for q = 0°, 180° B b

Magnitude Geometrically q B b AB = area of parallelogram

Magnetic Force on a Charge F = 0 unless charge is moving F = 0 if velocity is  to field F = maximum if velocity is  to field F  0 only if charge crosses B field lines F = qvB sin(q) in general If v or B reverse, direction of F reverses

Group Work What are the units of magnetic field B?

Cross Product Direction Curl right-hand fingers in direction of q Right-hand thumb points in direction of cross-product Not commutative A B a b q AB = –(BA)

Force Direction F = qv  B Right-Hand Rule SCI340 L46 Lorentz force Force Direction F = qv  B qv Source: Griffith, The Physics of Everyday Phenomena Right-Hand Rule

Origami Right Hand paper square creases: in out vectors fold over magnetic field current qv Force Lorenz vectors fold over

Group Question What is the direction of the force on the object moving with velocity v through magnetic field B? A. D. B + B. E. v C. F.

Group Question What is the magnitude of the force on object A compared to the magnitude of the force on object B? B A B v q v 2q

Group Work A particle with charge q has a velocity perpendicular to a uniform magnetic field. What will its subsequent path be? B v q

Force on a current §21.5

Force on a Current Moving charge Q with speed v in a length L of wire In time Dt, charges move a distance Dx = vDt The quantity of charge passing a point in time Dt is DQ = Q Dx/L = QvDt/L The current is I = DQ/Dt = Qv/L Qv = IL

Force on a Wire Qv = IL So F = Qv  B = IL  B

Group Question Two parallel wires carrying currents in the same direction attract each other. repel each other. have no effect on each other. Think of their magnetic fields and charge movements!

Force between parallel currents SCI340 L46 Lorentz force Force between parallel currents What is the force on this current? I  B

Force between parallel currents

Definition of Ampere If two parallel wires are held 1 m apart, with currents of 1 A through each wire, the attractive force between the wires is 2  10–7 N for each meter of length of the wires.

Torque on a loop §21.6

Torque on a Current Loop A parallelogram in a B field Any orientation I W L Opposite forces cancel Torques do not

Loop Dipole Moment Magnitude = m = IA Direction = right-hand rule I m

Effect of Torque The magnetic field “tries” to orient the current loop so that its magnetic dipole points in the direction of the field. Just like a dipole magnet in a field Because that’s what it is