Magnetic Effect of Current

1 P15-Class 15: OutlineHour 1:Magnetic ForceExpt. 6: Magnetic ForceHour 2:Creating B Fields: Biot-Savart2 P15-Last Time:Magnetic Fields& Magnetic Dipoles3 P15-Magnetic FieldsBq=×FvB􀁇􀁇􀁇Magnetic Dipoles Create and Feel B Fields:Also saw thatmoving charges feel a force:4 P15-What Kind of Motion Does this Lead to?5 P15-Cyclotron Motion(1) r : radius of the circle 2mvqvBr=mvrqB⇒=(2) T : period of the motion 22rmTvqBππ==2vqBfrmωπ===(3) ω : cyclotron frequency6 P15-Current Carrying Wires7 P15-Bq=×FvB􀁇􀁇􀁇Magnetic Force on Current-Carrying Wire()mcharges=×B􀁇()BI=×FLB􀁇􀁇􀁇chargems=×B􀁇8 P15-Demonstration:Jumping Wire9 P15-Magnetic Force on Current-Carrying WireCurrent is moving charges, and we know that moving charges feela force in a magnetic field10 P15-PRS Questions:5 Predictions For Experiment 611 P15-Experiment 6:Magnetic Force 12 P15-Mid-term Course Evaluation13 P15-Lab Summary:Currents FEEL Forces in Magnetic FieldsQuestion:What happens if currents are next to each other?14 P15-Demonstration:Parallel & Anti-Parallel Currents15 P15-How Do They Interact?Moving charges also createmagnetic fields!The current in one wire createsa magnetic field that is feltby the other wire. This is the rest of today’s focus(http://ocw.mit.edu/ans7870/8/8.02T/f04/vis(http://ocw.mit.edu/ans7870/8/8.02T/f04ualizations/magnetostatics/13-/visualizations/magnetostatics/14-ParallelWires/13-SeriesWires/14-Series_320.htmlParallel_Wires_320_f185.html))16 P15-Sources of Magnetic Fields:Biot-Savart17 P15-Electric Field Of Point ChargeAn electric charge produces an electric field: rˆ21ˆ4oqrπε=Er􀁇rˆ: unit vector directed from q to P18 P15-Magnetic Field Of Moving ChargeMoving charge with velocity v produces magnetic field:2ˆx4oqrµπ=vrB􀁇􀁇:ˆrrˆPunit vector directed from q to Ppermeability of free space70410Tm/Aµπ−=×⋅19 P15-The Biot-Savart LawCurrent element of length dscarrying current I produces a magnetic field:20ˆ4rdIrsBd×=􀁇􀁇πµ(http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/03-CurrentElement3d/03-cElement320.html)20 P15-The Right-Hand Rule #2ˆˆˆ×=zρφ21 P15-Animation: Field Generated by a Moving Charge (http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/01-MovingChargePosMag/01-MovChrgMagPos_f223_320.html)22 P15-Demonstration:Field Generated by Wire23 P15-Example : Coil of Radius RConsider a coil with radius Rand current IIIIPFind the magnetic field B at the center (P)24 P15-Example : Coil of Radius RConsider a coil with radius Rand current IIIIP1) Think about it:•Legs contribute nothingIparallel to r•Ring makes field into page2) Choose a ds3) Pick your coordinates4) Write Biot-Savart25 P15-Example : Coil of Radius RIn the circular part of the coil…ˆd⊥sr􀁇ˆ|d|ds→×=sr􀁇rˆs􀁇dIII02ˆ4dIdBrµπ×=sr􀁇Biot-Savart:024Idsrµπ=024IRdRµθπ=04IdRµθπ=26 P15-Example : Coil of Radius RConsider a coil with radius Rand current I04IddBRµθπ=2004IdBdBRπµθπ==∫∫()2000244IIdRRπµµθπππ==∫IIIθs􀁇d0into page2IRµ=B􀁇27 P15-Example : Coil of Radius RNotes:•This is an EASY Biot-Savart problem:•No vectors involved•This is what I would expect on examIIPIpage into20RIµ=B􀁇28 P15-PRS Questions:B fields Generated by Currents29 P15-Group Problem:B Field from Coil of Radius RConsider a coil with radius Rand carrying a current IWARNING:This is much harder than what I just did! Why??What is B at point P?30 P15-Field Pressures and Tensions:A Way To Understand the qVxBMagnetic Force31 P15-Tension and Pressures Transmitted by E and BFields(E or B):•Transmit tension along field direction (Field lines want to pull straight)•Exert pressure perpendicular to field (Field lines repel)32 P15-Example of E Pressure/Tension(http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/electrostatics/11-forceq/11-ForceQ_f0_320.html)Positive charge in uniform (downward) E fieldElectric force on the charge is combination of 1.Pressure pushing down from top 2.Tension pulling down towards bottom33 P15-Example of B Pressure/TensionPositive charge moving out of page in uniform (downwards) B field. Magnetic force combines:1.Pressure pushing from left 2.Tension pulling to right(http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/10-forcemovingq/10-ForceMovingQ_f0_320.html)