Physics 212 Lecture 13, Slide 1 Physics 212 Lecture 13 Forces and Torques on Currents

Physics 212 Lecture 13, Slide 2 Key Concepts: Forces & Torques on loops of current due to a magnetic field.Forces & Torques on loops of current due to a magnetic field. The magnetic dipole moment.The magnetic dipole moment. 05

Physics 212 Lecture 13, Slide 3 06 Force on a wire carrying current I Cross sectional area A, Length L Number of charges/m 3 = n Each charge moving at V avg Force on each charge Total force on wire Use

Current- carrying wire in uniform B field Out of page

Physics 212 Lecture 13, Slide 5 ACT ABCABC 08

Physics 212 Lecture 13, Slide 6 ABCABC ACT 10

Physics 212 Lecture 13, Slide 7 What is the force on section d-a of the loop? A)Zero B)Out of the page C)Into the page ACT 12

Physics 212 Lecture 13, Slide 8 Checkpoint 1a 13 ABCABC “The net force on any closed loop is zero.”

Physics 212 Lecture 13, Slide 9 In which direction will the loop rotate? (assume the z axis is out of the page) A)Around the x axis B)Around the y axis C)Around the z axis D)It will not rotate x y 15 Checkpoint 1b

Physics 212 Lecture 13, Slide 10 R F Checkpoint 1c 17 ABCDEABCDE y

Physics 212 Lecture 13, Slide 11 Magnetic Dipole Moment Area vector Magnitude = Area Direction uses right hand rule Magnetic Dipole moment 19

Physics 212 Lecture 13, Slide 12 The torque always wants to line  up with B ! B  turns  toward B x y z B  x y z 21

Physics 212 Lecture 13, Slide 13 B  In this case is out of the page (using right hand rule) In this case  is out of the page (using right hand rule) I B  x y z is up (turns  toward B) 22 Practice with  and 

Physics 212 Lecture 13, Slide 14 Biggest when 24 Checkpoint 2a Three different orientations of a magnetic dipole moment in a constant magnetic field are shown below. Which orientation results in the largest magnetic torque on the dipole?

Physics 212 Lecture 13, Slide 15 Potential energy of a magnetic dipole moment 27 Rotate  from  1 to  2

Lowest U  parallel to B Highest U  antiparallel to B B  U U = 0

Physics 212 Lecture 13, Slide 17 Checkpoint 2b 30 U = 0 U = -  Bcos   U = +  Bcos   Three different orientations of a magnetic dipole moment in a constant magnetic field are shown below. Which orientation has the most potential energy?

Physics 212 Lecture 13, Slide 18 ACT 30 cc aa aa Three different orientations of a magnetic dipole moment in a constant magnetic field are shown below. We want to rotate the dipole in the CCW direction. B First, consider rotating to position c. What are the signs of the work done by you and the work done by the field? A)W you > 0, W field > 0 B)W you > 0, W field < 0 C)W you 0 D)W you < 0, W field < 0  U > 0, so W field < 0. W you must be opposite W field Also, torque and displacement in opposite directions  W field < 0

Physics 212 Lecture 13, Slide 19 ACT 30 cc aa aa Consider rotating the dipole to each of the three final orientations shown. B Does the sign of the work done by you depend on which position (a, b, or c) the dipole is rotated to? A)Yes B)No The lowest potential energy state is with dipole parallel to B. The potential energy will be higher at any of a, b, or c.

Physics 212 Lecture 13, Slide 20Calculation A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known. How much does the potential energy of the system change as the coil moves from its initial position to its final position. Conceptual Analysis –A current loop may experience a torque in a constant magnetic field  =  X B –We can associate a potential energy with the orientation of loop U = -  ∙ B z x y B. 30˚ y z I initial final Strategic Analysis –Find  –Calculate the change in potential energy from initial to final a B 32

Physics 212 Lecture 13, Slide 21Calculation What is the direction of the magnetic moment of this current loop in its initial position? (A) (B) (C) (D) (A) +x (B) -x (C) +y (D) -y z x ● y A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known. z x y B. 30˚ y z I initial final a B z y. X  Right Hand Rule 34

Physics 212 Lecture 13, Slide 22Calculation What is the direction of the torque on the current loop in the initial position? (A) (B) (C) (D) (A) +x (B) -x (C) +y (D) -y A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known. z x y B. 30˚ y z I initial final a B B z y. X  36

Physics 212 Lecture 13, Slide 23Calculation What is the potential energy of the initial state? (A) 0 (A) U initial 0 A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known. z x y B. 30˚ y z I initial final a B z y  B  38

Physics 212 Lecture 13, Slide 24Calculation What is the sign of the potential energy in the final state? (A) 0 (A) U final 0 A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known. z x y B. 30˚ y z I initial final a B initial final z y  B   z y  B     40 Check:  moves away from B Energy must increase !

Physics 212 Lecture 13, Slide 25Calculation (A) (B) (C) What is the potential energy of the final state? A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known. z x y B. 30˚ z I initial final a B z y  B   44