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Transcript
Magnets and Charges Vector Direction Conventions Left Right 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 AB is perpendicular to both A and B Cross Product Magnitude a q A B = ab sin q A B b Maximum for q = 90° Zero for q = 0°, 180° Magnitude Geometrically a q A B b AB = 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 a q A B b • Curl right-hand fingers in direction of q • Right-hand thumb points in direction of crossproduct • Not commutative AB = –(BA) Force Direction F = qv B qv Source: Griffith, The Physics of Everyday Phenomena Right-Hand Rule Origami Right Hand vectors fold over qv current Force creases: in out Lorenz paper square magnetic field Group Question What is the direction of the force on the object moving with velocity v through magnetic field B? B A. D. B. E. C. F. + v Group Question What is the magnitude of the force on object A compared to the magnitude of the force on object B? A B q v B 2q v Group Work A particle with charge q has a velocity perpendicular to a uniform magnetic field. What will its subsequent path be? B q v Force on a Current • Moving charge q traverses a length L of wire in time t • Current I = q/t, speed v = L/t • Force = qvB = qLB/t = LIB I B 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 A. attract each other. B. repel each other. C. 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? IB 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.