# L9-1 - L9-1Now on to a mathematical description of magnetic...

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Unformatted text preview: L9-1Now on to a mathematical description of magnetic fields:- recall 2 ways to calculate electric field- here there are also two ways- dB =I ds…- ∫B·dl =….2ˆencEdQdEkrrQε=Φ=rintegrating over chargesintegral ruleintegrating over currentsintegral ruleYou can’t derive these laws – proven by experimentThe Biot-Savart Law:How do you make a magnetic field?Charges in motion create a magnetic field. A steady current Iflows in a circuit. What is the resulting magnetic field?IThe electric field dEproduced by a charge dqisdE= (1/4πμ)(dq/r2)r→→f8e5The Biot-Savartlaw says:The magnetic field dBproduced by a bit of circuit dscarrying current IisdB= (μ/4π)(I/r2)dsΧr The permeability constantisμ= 4π ×10-7T-m/Aexactly.→→→→ f8e5ˆˆGeneral meaningof Biot-Savart formuladB= (μ/4π)(I/r2)ds×r•r is unit vector from point on wire to point P •dspoints along wire indirection of current•dsxrgives a vector –= direction of dB at point Pthen integrate along wire Btot= ∫dB→→→→→→ˆˆField of a Long,Straight WireB= μI / 2πrUse Biot-Savart to compute:Field of a Long,Straight WireB= μI / 2πrField at distance rfrom long, straight wire carrying current IUse Biot-Savart to compute:Direction of B- around the wire(the field lines are circles)Use a right-hand rule:Thumb along current, thenfingers show B→The magnetic field at the position P points1. Down.2. Up.3. Out of the page.4. Into the page.The positive charge is moving straight out of the page. What is the direction of the magnetic field at the position of the dot?1. Right2. Left3. Up4. DownA straight wire carries 100 A. The magnetic field strength one foot (~1/3 m) away from this wire is approximately(just try for the order of magnitude)1. 0.07 T2. 0.007 T3. 7 G4. 70 G5. 0.7 GA straight wire along the yaxis carries current in the +ydirection. On the negative zaxis the direction of the magnetic field is1. +x2. -x3. +y4. -y4. -zFour long, straight wires run perpendicular to the plane of...
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L9-1 - L9-1Now on to a mathematical description of magnetic...

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