Download Magnetic Forces on Currents and Current Loops in a Uniform Magnetic Field and more Study notes Physics in PDF only on Docsity! Physics 102: Lecture 9, Slide 1 Currents and Magnetism Physics 102: Lecture 09 Physics 102: Lecture 9, Slide 2 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 5 force is zero out of the page into the page a b cd B 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. What is the direction of the force on section b-c of the wire? F Physics 102: Lecture 9, Slide 6 B I L F=IBLsin Here = 180° a b cd B I 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. Force on section c-d is zero! Same as a-b Physics 102: Lecture 9, Slide 7 force is zero out of the page into the page a b cd B I 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. What is the direction of the force on section d-a of the wire? F Physics 102: Lecture 9, Slide 10 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x ACT: Torque on Current Loop What is the torque on the loop below? 1) < IAB 2) = IAB 3) > IAB Physics 102: Lecture 9, Slide 11 Torque on Current Loop It is useful to define normal vector ⊥ to loop a b c d F F B B F F 𝜏= 𝐼𝐴𝐵 sin𝜃 Torque is: normal normal = 180 – 𝜏= 𝑁𝐼𝐴𝐵 sin𝜑 If there are N loops: = 𝐼𝐴𝐵 sin𝜑 Note torque will align normal parallel to B like a magnetic dipole!Even if loop is not rectangular, as long as it is flat a b c d F F normal S N Physics 102: Lecture 9, Slide 12 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 15 A long straight wire is carrying current from left to right. Near the wire is a charge q with velocity v 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) v I v (a) r • • r (b) F F ACT/Preflight 9.6 q q Physics 102: Lecture 9, Slide 16 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 ACT: Adding Magnetic Fields 1) Left 2) Right 3) Up 4) Down 5) Zero Physics 102: Lecture 9, Slide 17 Force between current-carrying wires B Another I towards us F Currents in same direction attract! I towards us B Another I away from us F Currents in opposite direction repel! Currents in same direction Currents opposite direction I towards us Physics 102: Lecture 9, Slide 20 𝐵= 𝜇0𝑛𝐼 B IB I 𝜇0 = 4𝜋× 10 −7𝑇𝑚 /𝐴 B is uniform everywhere inside of solenoid: n is the number of turns of wire/meter (n = N/L) B field lines look like bar magnet! Solenoid has N and S poles! Solenoids M ag ni tu de Di re ct io n • Use “Right-hand rule 2” • A solenoid consists of N loops of wire Physics 102: Lecture 9, Slide 21 (1) Attractive (2) Zero (3) Repulsive ACT: The force between the two solenoids is … Physics 102: Lecture 9, Slide 22 Summary of Right-Hand Rules B I B I r RHR 1 RHR 2 Alternate Force on moving q B field from current I Straight wire Solenoid I
