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Transcript
Physics 102: Lecture 09 Currents and Magnetism Physics 102: Lecture 9, Slide 1 Summary of Today • Last time: – Magnetic forces on moving charge • magnitude F = qvBsin() • direction: right-hand-rule • Today: – Magnetic forces on currents and current loops – Magnetic fields due to currents • long straight wire • solenoid Physics 102: Lecture 9, Slide 2 Force of B-field on Current • Force on 1 moving charge: – F = q v B sin() – Out of the page (RHR) B + v • Force on many moving charges: – F = q v B sin() = (q/t) (vt) B sin() = I L B sin() – Out of the page! Physics 102: Lecture 9, Slide 3 B + + + +v L = vt I = q/t Preflight 9.1 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 B I a b F=IBLsin Here = 0 What is the direction of the force on section a-b of the wire? force is zero out of the page into the page Physics 102: Lecture 9, Slide 4 I Preflight 9.2 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. c d F B I a b What is the direction of the force on section b-c of the wire? force is zero out of the page into the page Physics 102: Lecture 9, Slide 5 Force on loop 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 B a I b Force on section c-d is zero! Same as a-b Physics 102: Lecture 9, Slide 6 I F=IBLsin Here = 180° ACT: Force on loop (cont’d) 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. c d F B I a b What is the direction of the force on section d-a of the wire? force is zero out of the page into the page Physics 102: Lecture 9, Slide 7 Torque on Current Loop in B field c d F F F B I a a d c b F b The loop will spin in place! Look from here Preflights 9.3, 9.4: Net force on loop is zero. But the net torque is not! Physics 102: Lecture 9, Slide 8 B Torque on Current Loop The loop will spin in place! F F a a Recall from Phys 101: 𝜏 = 𝐹𝐿 sin 𝜃 F d ad d c L b c b F bc F B B w F F Force on sections b-c and a-d: F = IBw Torque on loop is t = L F sin() = I Lw B sin() Torque is: 𝜏 = 𝐼𝐴𝐵 sin 𝜃 Physics 102: Lecture 9, Slide 9 Lw = A ! ACT: Torque on Current Loop What is the torque on the loop below? 1) t < IAB 2) t = IAB 3) t > IAB Physics 102: Lecture 9, Slide 10 xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx Torque on Current Loop It is useful to define normal vector ⊥ to loop F F d d a a normal F normal f S f=0 c b F b f B N B c F f = 180 – Torque is: 𝜏 = 𝐼𝐴𝐵 sin 𝜃 = 𝐼𝐴𝐵 sin 𝜑 If there are N loops: 𝜏 = 𝑁𝐼𝐴𝐵 sin 𝜑 Even if loop is not rectangular, as long as it is flat Physics 102: Lecture 9, Slide 11 normal F Note torque will align normal parallel to B like a magnetic dipole! Current loops act like dipoles Orbits of electrons “spin” Electron orbit and “spin” are current loops Why some materials are magnetic Nuclear Magnetic Resonance (NMR) and MRI Physics 102: Lecture 9, Slide 12 ACT: Torque B B I (1) (2) Compare the torque on loop 1 and 2 which have identical area, and current. Area points out of page for both! 1) t1 > t2 2) t1 = t2 3) t1 < t2 f = 90 Physics 102: Lecture 9, Slide 13 t = I A B sin(f) Currents create magnetic fields • Straight wire carrying current I generates a field B at a distance r: −7 𝜇 = 4𝜋 × 10 𝑇𝑚/𝐴 0 𝜇 𝐼 𝐵= 0 2𝜋𝑟 • “Right-hand rule 2”: – Thumb of right hand along I – Fingers of right hand along r – Out-of-palm points along B “Permeability of free space” (similar to e0 for electricity) B r I (out of page) B field circles wire Physics 102: Lecture 9, Slide 14 Note: there are different versions of RHR ACT/Preflight 9.6 A long straight wire is carrying current from left to right. Near the wire is a charge q with velocity v q • (a) F v r q (b) • F r v I Compare magnitude of magnetic force on q in (a) vs. (b) a) has the larger force b) has the larger force c) force is the same for (a) and (b) Physics 102: Lecture 9, Slide 15 ACT: Adding Magnetic Fields Two long wires carry opposite current x What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”? 1) Left 2) Right Physics 102: Lecture 9, Slide 16 3) Up 4) Down 5) Zero Force between current-carrying wires Currents in same direction B F I towards us Another I towards us Currents in same direction attract! Physics 102: Lecture 9, Slide 17 Currents opposite direction B F I towards us Another I away from us Currents in opposite direction repel! 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() Perpendicular to v,B Field Lines + Opposites Physics 102: Lecture 9, Slide 18 Charges Attract Currents Repel ACT: Force between Wires What is the direction of the force on the top wire, due to the two below? 1) Left Physics 102: Lecture 9, Slide 19 2) Right 3) Up 4) Down 5) Zero Solenoids • A solenoid consists of N loops of wire B is uniform everywhere inside of solenoid: 𝜇0 = 4𝜋 × 10−7 𝑇𝑚/𝐴 𝐵 = 𝜇0 𝑛𝐼 n is the number of turns of wire/meter (n = N/L) • Use “Right-hand rule 2” B B I I Physics 102: Lecture 9, Slide 20 B field lines look like bar magnet! Solenoid has N and S poles! ACT: The force between the two solenoids is … (1) Attractive (2) Zero (3) Repulsive Physics 102: Lecture 9, Slide 21 Summary of Right-Hand Rules RHR 1 RHR 2 Force on moving q Alternate B field from current I Straight wire I B r I Solenoid B I Physics 102: Lecture 9, Slide 22