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MTE2 Wed 26, at 5:30-7:00 pm Ch2103 and SH 180 Contents of MTE2 ! ! ! ! ! ! ! ! ! ! Work of the electric force and potential energy Electric Potential and Field Capacitors and capacitance Current and resistance, Ohm’s law DC Circuits and Kirchoff’s laws RC circuits Lorentz force and motion of charge in a magnetic field Biot and Savart No Ampere’s law, No magnetic properties of matter Alternate Exams will be: Wed 26 2:30-4:00pm Lab room (Ch 3254) 6:00-7:30pm Lab room (Ch 3254 ) Study chapters 27-32 (no 32.6, 32.10, no 32.8 forces between wires) 2 This week Honor Lecture Magnetic Fields ! ! Susan Nossal: Climate change ! ! ! A vector quantity (B) compass needle traces B field lines and points towards N B-field lines start in N and go to S they do not start or stop (no magnetic monopoles Electric dipole Iron filings show pattern of B-field lines - 3 Earth’s A Magnet! Electric vs Magnetic Field Lines N geographic pole almost at magnetic S pole !S geographic pole almost at magnetic N pole ! ! ! A the N pole of a compass needle is attracted toward the geographic N pole (S pole of the B-field) Similarities ! Density gives strength ! Arrow gives direction ! Leave +, North ! Enter -, South Differences ! Start/Stop on electric charge ! No Magnetic Charge ! lines are continuous! + Charged particle in a B-field: Lorentz force The magnetic force r r r F = qv " B vector ‘cross product’ acts only a moving charged particle Units: N = C x m/s x Tesla Effect of uniform magnetic field ! Effect of uniform B-field on charged particle ! If charged particle is not moving - no effect ! If particle is moving: force perpendicular to both field and velocity ! the charge sign must be accounted for FB = q vB sin " ! F is zero when v and B are parallel or antiparallel ! F is a maximum when v and B are ! perpendicular ! ! 8 The magnetic force NEVER does work on the particle. Magnetic Force and Work Quick Quiz Magnetic force perpendicular to the particle displacement => the magnetic force does not do work! The three charges below have equal charge and speed, but are traveling in different directions in a uniform magnetic field. B field can alter direction of velocity, but not the speed or the kinetic energy Which particle experiences the greatest magnetic force? B x x x x x x B x x x x x x v x x x x x x B ######## v # # # # #v# # # F q q F q F=0 A) B) C) 1 2 3 D) Same 3 B F = q v B sin($) 2 1 9 Mass spectrometer and v selector Cyclotron Motion ! F " to v and B x x x x x xx x x x x x x x x x x xx x x x xv xB v F F ! particle path is a circle of radius R. ! a = v2/R is the centripetal acceleration ! R depends on m, q, v, B q R In how much time does the particle complete an orbit? F = ma v qB = R m 2# 2#m "= , T = period = T qB " = angular velocity = ! 11 ! 12 Experiment in Lab: motion of charges in B-field Magnetic Force on a Current e- 1) Turn on electron ‘gun’ Force on each charge ! Force on length ds of wire B R 1 2 mv = q"V 2 2) Turn on magnetic field B (Helmotz coils) ! %V qv " B qv " Ids dF = Ids " B ! ‘gun’ ! 3) Measure electron charge/mass as a function of !V, R and B m 2v 2 q m2 q R 2 = 2 2 = 2 "V 2 2 v 2 = 2 "V q B m q B m ! FB = I L " B ! ! ! q 2"V = m R 2B 2 ! 13 14 ! Torque on a current loop ‘Homopolar motor’ A homopolar motor has a B-field along the axis of rotation and an electric current produced by the battery that moves radially through the magnet. B Ids ! The resulting Lorentz force in the tangential direction produces a torque in the magnet, which is free to rotate with the attached screw. The name homopolar refers to the absence of polarity change. Consider current loop in magnetic field perpendicular to the plane of the loop => Zero net force ! ! Force on top path cancels force on bottom path (F = IBL) x x x Fx x x x x x x x x x x x x x x x x F x x x x x i x x x x x B x x x x F x F Force on right path cancels force on left path. (F = IBL) B F If plane of loop is not to B-field, there x is a torque on the loop (force couple as for electric dipole in E-field) FB = I L " B F F . 15 16 ! Calculation of Torque • Square loop has width W and length L (into the screen). The torque is given by: r r r r r " = r1 # F + r2 # F $w ' " = 2& F sin # ) %2 ( ! rxF F = IBL " # = IBLw sin $ = IBAsin $ ! ! A = wL = area of loop Potential Energy of Magnetic Dipole B I r $ x 1 w F F r2 . B $ x magnetic dipole moment direction: " to plane of the loop µ=AI according to RH rule (hands curls on current) • Note: if loop consists of N turns, µ = N A I w F $ µ ! Work must be done to change the orientation of a dipole (current loop) in the presence of a magnetic field. ! Define a potential energy U corresponding to this work (U=0 when magnetic dipole moment orthogonal to B-field = equilibrium position corresponding to max torque) B F . ! x w F 17 µ $ F . Quick Quiz Surprise! Which configuration has the greatest potential energy? µ B µ ! x B ! B ! µ x Electric current produces magnetic field Current (flow of electric charges ) in wire produces B-field. The magnetic field aligns compass needle 2 kind of magnetism due to permanent magnets and currents or the same? x Current &=0 & = µB &=0 U = -µB U=0 U = µB A) B) Magnetic field C) 1819 Hans Christian Oersted Magnetic field from a current Iron filings align with magnetic field lines Current loop as magnetic dipole A current loop is an electromagnet: it behaves like a permanent magnet. Two current loops with current in the same direction attract like 2 magnets (since the opposite poles are closer) Magnetic field loops around the current. (Right hand rule) 21 22 Field from a circular loop Biot-Sarvart Law For a single charge in motion ur B= For a wire with current µ0 qv # ur 4" r 2 At the center of the loop: dB = B out of page I ds ! µ ds # ur dB = 0 I 4" r2 ! ! Each element of current produces a contribution to the magnetic field. permeability of free space ! B= ! B= µ0 = 4 " #10$7 Tm / A = 1.257 #10$6 Tm / A 23 ! ! µ0 Idlsin # # = 90 o µ Idl $ $$% dB = 0 2 4" R 2 4" R qv " Ids r $ ! 20 µ0 I 4" R 2 # dl µ0 I µI 2"R = 0 2 4" R 2R ! Happy spring break to all! 25