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Magnetic Force Introduction Magnetic force on moving charge Examples
Magnetic deflection animation x and o diagrams More examples Magnetic force on current-carrying wire Still more examples
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Magnetism and Induction
Magnetism is weird, both for the force involved and its direction. It’s like a correction to electric forces when charges are in motion, and correction terms are always weird.* Electric affects charges, magnetism affects charges in motion Electric causes linear accelerations, magnetism causes sideways deflections (RH rule) Magnetism and Induction are very, very (societally) important! Motors, generators, loudspeakers, credit cards, hard drives, transformers….. *Can derive magnetic force from electric force and Einstein’s theory of relativity
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Magnetic Force on moving charge
Formal vector definition 𝑭=𝑞𝒗×𝑩 Force Magnitude 𝐹=𝑞𝑣𝐵𝑠𝑖𝑛𝜃 Maximum in v perpendicular to B Zero when v parallel to B Like torque, only cares about ⊥ component Force Direction Direction right-hand rule Positive vs. negative charge B units Tesla = 1 N/A-m (show units) Units 𝑇𝑒𝑠𝑙𝑎= 𝑁 𝐴∙𝑚 = 𝑁∙𝑠 𝐶∙𝑚
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Right-hand rule Hand in direction of v Bend in direction B
Thumb points in direction of F Alternative right hand rules
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Example - Magnetic Force on moving charge
A proton/electron moves straight north at 105 m/s in a 1 T magnetic field pointed west to east. What is the magnitude and direction of the force? 𝐹=𝑞𝑣𝐵𝑠𝑖𝑛𝜃 = 1.6∙ 10 −19 𝐶 ( 𝑚 𝑠) 1 𝑁 𝑠 𝐶 𝑚 sin(90) =1.6∙ 10 −14 𝑁 Direction Proton: straight down into the ground Electron: straight up in air
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Example 2 - Magnetic Force on moving charge
It feels no force when its moving in the direction or against the direction of the field (ϴ = 0 or 180). Thus the field must point north to south, or south to north Direction v up B to north gives F to west Magnitude 𝐵= 𝐹 𝑞𝑣 = 8∙ 10 −14 (1.6∙ 10 −19 𝐶)(5∙ 𝑚 𝑠 ) =0.1 𝑇 F v
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Magnetic force video mp4 video
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X’s and O’s Simplify diagrams – B field out of or into plane of paper
B coming out B going in (+) deflects to right (-) deflects to right
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Circular motion in magnetic field
RHR (flip sign) center of circle Set mag force = mv2/r 𝑞𝑣𝐵= 𝑚 𝑣 2 𝑟 𝑟= 𝑚𝑣 𝑞𝐵 = (9.1∙ 10 −31 𝑘𝑔)(2∙ 𝑚 𝑠 ) (1.6∙ 10 −19 𝐶)(0.01 𝑁 𝑠 𝐶 𝑚) =0.011 𝑚 𝑟𝑎𝑑𝑖𝑢𝑠
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Circular motion in magnetic field
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Examples – Force on Moving Charge
Problem 11 – Direction of force for (-) charge Problem 12 – Direction of field for (+) charge
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Problem Answers
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More examples – Force on Moving Charge
To accelerate in electric field 𝑞𝑉= 1 2 𝑚 𝑣 2 𝑣= 2𝑞𝑉 𝑚 To deflect in magnetic field 𝑞𝑣𝐵= 𝑚 𝑣 2 𝑟 𝑟= 𝑚𝑣 𝑞𝐵 = 𝑚 𝑞𝐵 2𝑞𝑉 𝑚 = 1 𝐵 2𝑚𝑉 𝑞 Double mass, radius goes up by 2 Quadruple mass, double charge, radius goes up by 2
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Magnetic Deflection
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Magnetic Deflection
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Force on Current-carrying wire
For single charge 𝐹=𝑞𝑣𝐵𝑠𝑖𝑛𝜃 For many charges 𝐹=𝑁𝑞 𝑣𝐵𝑠𝑖𝑛𝜃 Rewriting velocity 𝐹=Nq 𝐿 𝑡 𝐵𝑠𝑖𝑛𝜃= 𝑁𝑞 𝑡 𝐿𝐵𝑠𝑖𝑛𝜃 First term is just current 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛𝜃
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Summary – 2 magnetic force laws
For single charge 𝐹=𝑞𝑣𝐵𝑠𝑖𝑛𝜃 For current-carrying wire 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛𝜃
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Example 20-1 𝐹=𝐼𝐿×𝐵 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛𝜃 = 30 𝐴 (.12 𝑚) 0.9 𝑁 𝐴 𝑚 𝑠𝑖𝑛60 =2.8 𝑁
= 30 𝐴 (.12 𝑚) 0.9 𝑁 𝐴 𝑚 𝑠𝑖𝑛60 =2.8 𝑁 Direction: into page
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Example 20-2 3.48∙ 10 −2 𝑁= 0.245 𝐴 (.1 𝑚) 𝐵 𝑠𝑖𝑛90 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛𝜃
𝐵=1.42 𝑁 𝐴 𝑚 =1.42 𝑇 Current direction: CCW Force on sides
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Problem 7 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛(90) 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛(80)
90° w.r.t. field ° w.r.t. field 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛(90) 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛(80) 𝐼= 𝐹 𝐿𝐵 = 6.5∙ 10 −2 𝑁 0.1𝑚 𝑁 𝐴 𝑚 =4.06 𝐴 𝐹= 4.06𝐴 0.1 𝑚 𝑁 𝐴 𝑚 sin(80) Force: toward viewer =6.4∙ 10 −2 𝑁 toward viewer
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Magnetron - Microwave ovens
Accelerated radially by radial Electric Field Spun circularly by crossed magnetic field. Interacts with resonant cavities around perimeter. 𝐹=𝑞𝑣×𝐵
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Magnetron - Details Magnets top and bottom
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Magnetron - History Amazon.com Tuxedo Park : A Wall Street Tycoon and the Secret Palace of Science That Changed the Course of World War II Paperback – May 6, 2003 by Jennet Conant (Author) The untold story of an eccentric Wall Street tycoon and the circle of scientific geniuses he assembled before World War II to develop the science for radar and the atomic bomb. Together they changed the course of history. helped defend Britain from the Blitz! Could now put radar in planes!
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Magnetism and Induction Flowchart
law change field Current force direct examples Force Law 1 B → qv → F = qv x B RHR 1 charge deflection picture tube Force Law 2 i → F = il x B 2 wires, motor, loudspeaker Ampere’s Law B = μoi/2πr ← i RHR 2 electromagnet solenoid Faraday Induction d/dt → Φ = B*A → ε = dΦ/dt i = ε/R Lentz generator transformer Magnetic field plus moving charge/current creates force
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