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Transcript
Physics 102: Lecture 09 Currents and Magnetism • • • • Exam 1 Monday night Conflicts, etc.—see course home page Be sure to bring your ID and go to correct room Review Sunday, 3-5 PM, Rm. 141 – I will work through HE1 from last semester (fall ‘10) – To be most useful, you should work the exam yourself prior to the review 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 60% 25% 15% 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 8% 20% 72% 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 t=0 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 S c b F b normal f f=0 B N f=0 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 normal f F B F F Note torque will align normal parallel to B like a magnetic dipole! B 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. Normal vector 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 B q (b) • F r v I Compare magnitude of magnetic force on q in (a) vs. (b) 34% a) has the larger force 50% b) has the larger force c) force is the same for (a) and (b) 16% 𝜇0 𝐼 Same 𝐵 = 2𝜋𝑟 Physics 102: Lecture 9, Slide 15 Same 𝐹 = 𝑞𝑣𝐵 sin 𝜃 = 90 for (a) and (b)! Same magnitude Different directions ACT: Adding Magnetic Fields Two long wires carry opposite current B 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 N S 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 Look at field lines, opposites attract. Look at currents, same direction attract. 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