Magnetic Fields: Understanding Force on Charged Particles and Current-Carrying Wires, Study notes of Geology

Download Magnetic Fields: Understanding Force on Charged Particles and Current-Carrying Wires and more Study notes Geology in PDF only on Docsity! Lecture 19 Chapter 29 Magnetic Fields Review • Force due to a magnetic field is • Charged particles moving with v ⊥ to a B field move in a circular path with radius, r • Cyclotrons and synchrotrons BvqFB rrr ×= qB mvr = Magnetic Fields (48) • Substitute this for q in • Velocity is drift velocity, vd φφ sinsin B v iLvBqvF d d dB == r dv Liitq == BvqFB rrr ×= Magnetic Fields (49) • Force on a current is • Vector L points along wire in the direction of the current • Force on a single charge is φsiniLBFB = r BLiFB rrr ×= BvqFB rrr ×= Magnetic Fields (50) • Checkpoint #5 – What is the direction of the B field so FB is maximum? • Where’s the maximum? • What’s the direction of B ? Use right-hand rule B points in -y φsiniLBBLiFB =×= rrr 90,1sin == φφ B Magnetic Fields (53) • Force is in opposite directions for long sides of the loop • Forces don’t cancel because they don’t share a common line of action • Instead produce have a net torque and the loop rotates iaBFB = r Magnetic Fields (54) • Now rotate loop slightly so short sides are no longer || to B • Short sides: – FB ≠ 0 instead – Equal but opposite FB s – Cancel each other since common line of action through center of loop φsiniLBBLiFB =×= rrr Magnetic Fields (55) • Now rotate loop slightly so short sides are no longer || to B • Long sides: – i is still ⊥ B so iLBBLiFB =×= rrr iaBFB = r Magnetic Fields (58) • Total torque is sum of torques for each long side • Area of loop is abA = θθτ sin 2 sin 2 biaBbiaB += θτ siniabB= θτ siniAB=so Magnetic Fields (59) • Torque tends to rotate loop so to align n with B field • Electric motor – oscillate polarity of B field to keep loop spinning • Torque for single loop • Replace single loop with coil of N loops or turns θτ siniAB= θττ sin)( BNiAN ==′ Magnetic Fields (60) • Define the magnetic dipole moment to be • Torque becomes • Analogous to • A magnetic dipole in a magnetic field has a magnetic potential energy, U • Analogous to NiA=µ BB rr ×== µθµτ sin Ep rr ×=τ EpU rr •−= BU rr •−= µ