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2049_ch29B - B be magnetic field and ds be differential...

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PLAN 1. Ampere’s law 2. Applications Require a high symmetry. Magnetic field due to i in a long straight wire — again. (Faster. No need to assume 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.)
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Electricity vs Magnetism Electricity Coulomb’s law Ù Gauss’ law Magnetism Biot-Savart law Ù Ampere’s law Plus: B v q F r r r × = B
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Ampere’s Law Take arbitrary path around set of currents – Let i enc be total enclosed current (+ up, down) – Let
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Unformatted text preview: 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) B r Not included in i enc s d r θ Q1 Which of the three loops has the largest magnitude of Amperian integral? Check Point Q2 The smallest? d b Example 2: Inside the Wire • F i n d B vs r inside long wire, assuming uniform current r R Example 3: Solenoid Loosely wound and short Tightly wound and long (~infinitely long)...
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