Electricit & Magnetism Lecture 13 Toda s Concept: Torques Electricit & Magne9sm Lecture 13, Slide 1
Extra Deadlines Extra deadlines have been set up for Prelectures and Checkpoints that happened last week. Please do them if ou haven t. but...
Torque Review Compare the torques? ~ = ~R ~F ~ = R? F R R R Torque(A) > Torque() > Torque(C)
Last Time: This Time: qv and IL have same Dimensions! F I x Electricit & Magne9sm Lecture 13, Slide 2
Clicker Question A square loop of wire is carring current in the clockwise direction. There is a horiontal uniform magnetic field pointing to the right. What is the force on section a-b on the loop? A. Zero. AOut of page C. Into the Page C Electricit & Magne9sm Lecture 13, Slide 3
Clicker Question A square loop of wire is carring current in the clockwise direction. There is a horiontal uniform magnetic field pointing to the right. What is the force on section b-c on the loop? A. Zero A. Out of page C. Into the Page C Electricit & Magne9sm Lecture 13, Slide 4
Clicker Question A square loop of wire is carring current in the clockwise direction. There is a horiontal uniform magnetic field pointing to the right. What is the force on section c-d on the loop? A. Zero. Out of page C. Into the Page Electricit & Magne9sm Lecture 13, Slide 5
CheckPoint 2 A square loop of wire is carring current in the clockwise direction. There is a horiontal uniform magnetic field pointing to the right. What is the direction of the net force on the loop? A. Zero. Out of page C. Into the Page Electricit & Magne9sm Lecture 13, Slide 6
CheckPoint 4 A square loop of wire is carring current in the clockwise direction. There is a horiontal uniform magnetic field pointing to the right. x In which direc9on will the loop rotate? (assume the axis is out of the page) A) Around the x axis ) Around the axis C) Around the axis D) It will not rotate Electricit & Magne9sm Lecture 13, Slide 7
CheckPoint 6 A square loop of wire is carring current in the clockwise direction. There is a horiontal uniform magnetic field pointing to the right. into page out of page What is the direc9on of the net torque on the loop? A) up (on page) ) down (on page) C) out of page D) into page E) net torque is ero Electricit & Magne9sm Lecture 13, Slide 8
Magnetic Dipole Moment Area vector Magnitude = Area Direc9on uses R.H.R. Magne9c Dipole moment Electricit & Magne9sm Lecture 13, Slide 9
µ Makes Torque Eas! The torque alwas wants to line µ up with! turns µ toward x µ µ x turns µ toward Electricit & Magne9sm Lecture 13, Slide 10
Practice with µ and τ µ I In this case µ is out of the page (using right hand rule) is up (turns µ toward ) x µ Electricit & Magne9sm Lecture 13, Slide 11
Practice with µ and τ I µ In this case µ is IN to the page (using right hand rule) x µ is down (turns µ toward ) Electricit & Magne9sm Lecture 13, Slide 11
CheckPoint 8 Electricit & Magne9sm Lecture 13, Slide 12
Magnetic Field does Work on Current-carring wire From Phsics 140: From Phsics 141: W = Z /2 µ sin d = µ cos = µ Text U 1.0000 0.7500 Define U = 0 at posi9on of maximum torque U = µ 0.5000 0.2500 0-0.2500-0.5000-0.7500-1.0000 angle ( ) 0 45 90 135 180 µ Electricit & Magne9sm Lecture 13, Slide 13
CheckPoint 10 φ θ U = µcosθ U = +µcosφ U = 0 Which orientation has the lowest potential energ? Electricit & Magne9sm Lecture 13, Slide 14
CheckPoint 12 θ a φ a θ c Y YOU Y FIELD Y WHOM? C): W b f ield = U = U i U f U = µ ): A): Electricit & Magne9sm Lecture 13, Slide 15
How much does the poten8al energ of the sstem change as the coil moves from its ini8al posi8on to its final posi8on. Calculation A square loop of side a lies in the x plane with current I as shown. The loop can rotate about x axis without fric9on. A uniform field points along the + axis. Assume a, I, and are known. x a ini9al I 30. final Conceptual Analsis A current loop ma experience a torque in a constant magne9c field τ = µ X We can associate a poten9al energ with the orienta9on of loop U = µ Strategic Analsis Find µ Calculate the change in poten9al energ from ini9al to final Electricit & Magne9sm Lecture 13, Slide 16
Calculation A square loop of side a lies in the x plane with current I as shown. The loop can rotate about x axis without fric9on. A uniform field points along the + axis. Assume a, I, and are known. x a initial ini9al I 30. final What is the direc9on of the magne9c moment of this current loop in its ini9al posi9on? A) +x ) x C) + D) Electricit & Magne9sm Lecture 13, Slide 17
Calculation A square loop of side a lies in the x plane with current I as shown. The loop can rotate about x axis without fric9on. A uniform field points along the + axis. Assume a, I, and are known. x a ini9al I µ 30. final What is the direc9on of the torque on this current loop in the ini9al posi9on? A) +x ) x C) + D) Electricit & Magne9sm Lecture 13, Slide 18
U = µ Calculation A square loop of side a lies in the x plane with current I as shown. The loop can rotate about x axis without fric9on. A uniform field points along the + axis. Assume a, I, and are known. x a ini9al I 30. final What is the poten9al energ of the ini9al state? A) U initial < 0 ) U initial = 0 C) U initial > 0 Electricit & Magne9sm Lecture 13, Slide 19
Calculation A square loop of side a lies in the x plane with current I as shown. The loop can rotate about x axis without fric9on. A uniform field points along the + axis. Assume a, I, and are known. U = µ x a initial ini9al I µ 30. µ final What is the poten9al energ of the final state? A) U final < 0 ) U final = 0 C) U final > 0 Electricit & Magne9sm Lecture 13, Slide 20
Calculation A square loop of side a lies in the x plane with current I as shown. The loop can rotate about x axis without fric9on. A uniform field points along the + axis. Assume a, I, and are known. U = µ x a ini9al I µ 30. µ final What is the poten9al energ of the final state? A) ) C) U 1.0000 0.7500 0.5000 0.2500 0-0.2500-0.5000-0.7500-1.0000 0 45 90 135 180 angle ( ) Electricit & Magne9sm Lecture 13, Slide 21