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Physics 1161: Lecture 13 Currents and Magnetism • Textbook Sections 22-4 – 22-7 Force of B-field on Current • Force on 1 moving charge: – F = q v B sin(q) – Out of the page (RHR) + • Force on many moving charges: – F = (q/t)(vt)B sin(q) = I L B sin(q) v q B + + + +v – Out of the page! L = vt I = q/t Preflight 13.1 A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A-B and C-D. B C D q B A I B I F=ILBsinq Here q = 0. What is the direction of the force on section A-B of the wire? force is zero 49% out of the page 36% into the page 15% Preflight 13.2 A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A-B and C-D. v C D F X I A B B B Palm into page. F What is the direction of the force on section B-C of the wire? force is zero 13% out of the page 38% into the page 50% Torque on Current Loop in B field C D • F F X B I A F A B C D B F The loop will spin in place! Look from here Preflights 13.3, 13.4 Net force on loop is zero. But the net torque is not! 78% Torque on Current Loop in B field C D • F F F X B W A f A I B L Force on sections B-C and A-D: F = Torque on loop is t = 2 x (L/2) F sin(f) = (length x width = area) Torque is t= LW = A ! C D B F Torque on Current Loop in B field C D • F F X B W A F f A I B B L C D L/2 L/2 Force on sections B-C and A-D: F = IBW Torque on loop is t = 2 x (L/2) F sin(f) = ILWB sin(f) (length x width = area) Torque is t = I A B sin(f) LW = A ! F Torque on Current Loop Magnitude: F t = I A B sinf between normal and B Direction: f B F Torque tries to line up the normal with B! (when normal lines up with B, f=0, so t=0! ) Even if the loop is not rectangular, as long as it is flat: t = N I A B sinf. # of loops (area of loop) Compare the torques on loops 1 and 2 which have identical areas and currents. 1. t1 > t2 2. t1 = t2 3. t1 < t2 0% 1 0% 2 0% 3 Compare the torques on loops 1 and 2 which have identical areas and currents. 1. t1 > t2 2. t1 = t2 3. t1 < t2 t = I A B sinf Area points out of page for both! f = 90 degrees 0% 1 0% 2 0% 3 Currents Create B Fields Magnitude: 0I B 2r B 0 4 10 7 Tm / A Current I OUT r • r = distance from wire Right-Hand Rule-2 Thumb: along I Fingers: curl along B field lines Lines of B Right Hand Rule 2! I wire Fingers give B! Preflight 13.6 A long straight wire is carrying current from left to right. Near the wire is a charge q with velocity v v v • (a) F r B • (b) • F I r Compare magnetic force on q in (a) vs. (b) (a) has the larger force 28% (b) has the larger force 55% force is the same for (a) and (b) 0I same B 2r same F qvB sin q 18% θ is angle between v and B (θ = 90° in both cases) Two long wires carry opposite current. What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”? x 1. 2. 3. 4. 5. Left Right Up Down Zero x 0% 1 0% 0% 2 3 0% 0% 4 5 Two long wires carry opposite current. What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point B marked “X”? x 1. 2. 3. 4. 5. Left Right Up Down Zero x 0% 1 0% 0% 2 3 0% 0% 4 5 Force between current-carrying wires I towards us • F B • Another I towards us Conclusion: Currents in same direction attract! I towards us • B F Another I away from us Conclusion: Currents in opposite direction repel! Note: this is different from the Coulomb force between like or unlike charges. Comparison: Electric Field vs. Magnetic Field Source Acts on Force Direction Electric Magnetic Charges Charges F = Eq Parallel E Moving Charges Moving Charges F = q v B sin(q) Perpendicular to v,B Charges Attract Currents Repel Field Lines Opposites Magnetic Fields of Currents • http://hyperphysics.phyastr.gsu.edu/hbase/magnetic/magfie.html#c1 Right Hand Rule 3 Magnetic Field of Solenoid B Field Inside Solenoids Magnitude of Field anywhere inside of solenoid : n is the number of turns of wire/meter on solenoid. 0 = 4 x10-7 T m /A (Note: N is the total number of turns, n = N / L) Right-Hand Rule for loop/solenoid Fingers – curl around coil in direction of conventional (+) current Thumb - points in direction of B along axis Magnetic field lines look like bar magnet! Solenoid has N and S poles! B=0 n I Preflight 13.8 What is the direction of the magnetic field produced by these solenoids? (1) to the Right (2) to the Left 65% 35% Right Hand Rule! What is the net force between the two solenoids? 1. Attractive 2. Zero 3. Repulsive 0% 1 0% 2 0% 3 What is the net force between the two solenoids? 0% 1 1. Attractive 2. Zero 3. Repulsive Look at field lines, opposites attract. Look at currents, same direction attract. 0% 2 0% 3