The shadow of electricity Magnetism The shadow of electricity

Magnetic Force Magnets apply forces to each other. Opposite poles attract, like poles repel.

CPS Question The magnitude of the force between magnetic poles is the same at all distances. becomes stronger as the poles come closer. becomes weaker as the poles come closer.

Magnetic Field Lines Conventions as with electric field lines. direction is direction of force on a north pole strong field where lines are close together Field lines point from North to South pole.

Group Work What happens to a dipole magnet in a uniform magnetic field? B N S

Naming the poles N = north-seeking Earth’s north pole is a south pole!

Magnets and Charges

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 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

Group Work A current runs through one wire of a pair of side-by-side wires. What is the direction of the resulting magnetic field at the location of the other wire? I ?

Group CPS 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 What is the force on this current? I  B

Force between parallel currents