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Applications of Ampere’s Law: Magnetic Fields in Current-Carrying Wires and Solenoids

Explore the magnetic field outside and inside a long straight wire and solenoid using Ampere's Law. Learn about magnetic fields of solenoids and toroidal solenoids. Practice examples and checkpoints provided.

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Applications of Ampere’s Law: Magnetic Fields in Current-Carrying Wires and Solenoids

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  1. Applications of Ampere’s Law Ex 26.8 Field outside and inside a long straight current- carrying wire Ex 26.9 Field outside a current sheet Ex 26.10 Field of a solenoid Fig 26.39 Field of a toroidal solenoid This lecture

  2. I EXAMPLE 26.8: A long straight wire of radius R carries a current I that is uniformly distributed over the circular cross section of the wire. Find the magnetic field both (a) outside and (b) inside the wire. I

  3. Magnetic field of a solenoid We can use Ampere’s Law. Take the loop with sides abcd and integrate along each side. Only side ab contributes. In bc and da, B is perpendicular to dl. In cd B = 0 (approx). Bh = μ0Ienc Bh = μ0 i N B = μ0in (n = N/h, number of turns per unit length)

  4. N S Graph of the magnetic field on the axis inside a solenoid versus the position x on the axis. The field is nearly constant except near the ends. Magnetic fields of a solenoid. They are identical to those of a bar magnet of the same shape.

  5. Toroid Read p457 Apply Ampere’s Law to circle of radius r

  6. CHECKPOINT: The figure shows three long, straight, parallel, equally spaced wires with identical currents either into or out of the page. Rank the wires according to the magnitude of the force on each due to the currents in the other two wires. Answer: B, C, A

  7. CHECKPOINT: The figure shows three equal currents i, two parallel, one anti-parallel, and four Amperian loops. Rank the loops according to the magnitude of along each, greatest first. Answer: D, A = C, B

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