Physics 213 General PhysicsPowerPoint PresentationSlide 3Slide 4Torque on a Current Loop, The Standard ConventionSlide 6Slide 7MotorsSlide 9Slide 10Slide 11Reverse the current and field.Slide 13Magnetic Fields – Long Straight WireDirection of the Field of a Long Straight WireMagnitude of the Field of a Long Straight WireAmpère’s Law, and Field from CurrentsAmpère’s Law to Find B for a Long Straight WireMagnetic Force Between Two Parallel ConductorsMagnetic Force Between Two Parallel Conductors, DerivedForce Between Two Conductors, contSlide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Magnetic MaterialsDemoTypes of Magnetic MaterialsMagnetic Effects of Electrons – SpinsFerromagnetic DomainsSlide 35Slide 36Slide 37Slide 38Physics 213General PhysicsLecture 102Last Meeting: Lorentz Force and TorqueToday: Review Torque, Magnetic Field of Conductors and Currents, Ampere’s Law, Solenoid, and Magnetic Materials34θ┴θ*Important: This is not the same as in the previous slide.is now the angle between the radius vector and the force vector. 5Torque on a Current Loop,The Standard Convention Applies to any shape loopN is the number of turns in the coil Torque has a maximum value of NBIAWhen = 90°Torque is zero when the field is perpendicular to the plane of the loop6xˆyˆzˆIBsinBIANDetermining Magnetic Moments and Torques for a Current LoopDirections are always determined with right-hand rule.Magnitudes are given by7 ┴μ =μμθθ8Motors9μsin B Review10IxˆyˆzˆBxˆyˆzˆBxˆyˆzˆB(A)(B) (C) It will not rotate.11IxˆyˆzˆBxˆyˆzˆBxˆyˆzˆB(A)(B) (C) It will not rotate.12IxˆyˆzˆBxˆyˆzˆBxˆyˆzˆB(A)(B) (C) It will not rotate.Reverse the current and field.1. CW 2. CCW3. It will not rotatexˆyˆzˆBCCWReverse the current and field.Magnetic Fields – Long Straight WireA current-carrying wire produces a magnetic fieldThe compass needle deflects in directions tangent to the circleThe compass needle points in the direction of the magnetic field produced by the currentDirection of the Field of a Long Straight WireRight Hand RuleGrasp the wire in your right handPoint your thumb in the direction of the currentYour fingers will curl in the direction of the fieldMagnitude of the Field of a Long Straight WireThe magnitude of the field at a distance r from a wire carrying a current of I isµo = 4 x 10-7 T.m / Aµo is called the permeability of free space2oIBrAmpère’s Law, and Field from CurrentsChoose an arbitrary closed path around the currentSum all the products of B|| Δℓ around the closed pathB|| Δℓ = µo IAmpère’s Law to Find B for a Long Straight WireUse a closed circular pathThe circumference of the circle is 2 r This is identical to the result previously obtained2oIBrMagnetic Force Between Two Parallel ConductorsThe force on wire 1 is due to the current in wire 1 and the magnetic field produced by wire 2The force per unit length is:1 22oI IFdMagnetic Force Between Two Parallel Conductors, DerivedThe force on wire 1F1 = I1 B ℓ sin θ B produced by wire 2sin=1, so1 22oI IFddIB220Force Between Two Conductors, contParallel conductors carrying currents in the same direction attract each other Parallel conductors carrying currents in the opposite directions repel each otherDemo of two current-carrying wires attracting/repelling.2223Circular current loops act like Magnetics, with a N and S pole.242526270 0NB =μ NI B= Illm�2829Magnetic MaterialsDemoMagnetic materials.Types of Magnetic MaterialsFerromagneticPermanent magnetic moments. Repel or attract depending on orientationParamagneticInduced magnetism in same direction as applied field. Materials are attracted to magnets.DiamagneticInduced magnetism in opposite direction as applied field. Materials are repelled. S N S N S N S N S N S N NS S N S N NSMagnetic Effects of Electrons – Spins Electrons also have spinThe classical model is to consider the electrons to spin like topsIt is actually a quantum effectFerromagnetic DomainsRandom alignment (left) shows an unmagnetized materialWhen an external field is applied, the domains aligned with B grow (right)Each domain acts like a little magnet with a N and S pole. Arrows below represent the magnetic moment.NSA loop of wire with a weight of 1.47 N is oriented vertically and carries a current I = 1.75 A. A segment of the wire passes through a magnetic field directed into the plane of the page as shown. The net force on the wire is measured using a balance and found to be zero. What is the magnitude of the magnetic field?(a) zero tesla (d) 1.5 T(b) 0.51 T (e) 4.2 T(c) 0.84 TXThe magnetic force is pointing upwards and cancels the gravitational force:1.471.474.20(1.75 )(0.20 )B gF BIl F NNB TA m= = == =Two long, straight, parallel wires separated by a distance d carry currents in opposite directions as shown in the figure. The bottom wire carries a current of 6.0 A. Point C is at the midpoint between the wires and point O is a distance 0.50d below the 6-A wire as suggested in the figure. The total magnetic field at point O is zero tesla.1. Determine the value of the current, I, in the top wire.(a) 2 A (c) 6 A (e) This cannot be determined since(b) 3 A (d) 18 A the value of d is not specified.X2. Determine the magnitude of the magnetic field at point C if d = 0.10 m.(a) 2.4x10–5 T (c) 9.6x10–5 T (e) 1.4x10–4 T(b) 4.8x10–5 T (d) 1.1x10–4 TX0 01 2(6.0 ),2 (1.5 ) 2 (0.5 )3 (6.0 ) 18.0I AB Bd dI A Am mp p= = == � =07518.0 6.0( ) ( )2 0.5 0.5(4 10 / )(24.0 ) 2 0.05 9.60 10A AB outd dTm A AmTmppp--= +�=�=
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