PLAN1. Ampere’s law2. Applications Require a high symmetry.♣ Magnetic field due to i in a long straightwire — again. (Faster. No need toassume that the wire diameter is zero.)♣ Magnetic field inside the wire.♣ Solenoid.♣ Toroid. 3. Magnetic field of a single coil. (Only along the symmetry axis. But you need to use the Biot-Savart law.)☺Electricity vs MagnetismElectricityCoulomb’s law Ù Gauss’ lawMagnetismBiot-Savart law Ù Ampere’s lawPlus:BvqFrrr×=BAmpere’s Law• Take arbitrary path around set of currents–Let iencbe total enclosed current (+ up, − down)–Let B be magnetic field, and ds be differential length along path (couterclockwise according to the right hand rule)• Only currents inside path contribute!– 5 currents inside path (included)– 1 outside path (not included)BrNot included iniencsdrθQ1 Which of the three loops has the largest magnitude of Amperian integral?Check PointQ2 The smallest?dbExample 2: Inside the Wire•Find B vs r inside long wire, assuming uniform currentrRExample 3: SolenoidLoosely wound and shortTightly wound and long (~infinitely
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