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Biot-Savart Law, Ampère’s Law

Biot-Savart Law, Ampère’s Law. Fields and forces for current in straight wires Ampère’s Law. Example 1: Long parallel wires. L. a. b. I 1. d. I 2. Find force on current I 1 in segment ab due to current I 2 (magnitude & direction). (Take I 1 = 20A, I 2 =30A, d=0.01m, L=1.5m).

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Biot-Savart Law, Ampère’s Law

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  1. Biot-Savart Law, Ampère’s Law • Fields and forces for current in straight wires • Ampère’s Law

  2. Example 1: Long parallel wires L a b I1 d I2 Find force on current I1 in segment ab due to current I2 (magnitude & direction) (Take I1 = 20A, I2=30A, d=0.01m, L=1.5m)

  3. Solution

  4. I2 Quiz The two long wires shown cross at right angles. The horizontal wire 1 is fixed.How will the red wire move when the currents are turned on?A) LeftB) RightC) Rotate clockwiseD) Rotate counter-clockwiseE) It won’t move I1

  5. Ampère’s Law (an integral theorem) For any closed path: The current flows through the surface bordered by the path. Positive current is out of the page through the shaded surface (right hand rule) direction of integration determines positive current direction

  6. Calculating B from Ampere’s Law For a few simple shapes, we can calculate the field B easily from Ampere’s Law. The steps: • use symmetry to choose an appropriate path • determine the direction of B from RHR. • calculate (in terms of |B|) • calculate Iencircled • apply Ampere’s Law to get B Ampere’s Law holds only for steady currents

  7. Question: Long Straight Wire On which of the curves C1, C2, and C3 is C 2 B I • i) smallest • largest • zero C 1 C 3

  8. Example 2: Long Straight Wire Show that the field produced by a current I in a long straight wire at distance r from the wire is: Steps:

  9. Solution I B ds field line path of integration

  10. Example 3: Wire, radius R, uniform current density R x x x x x x x x x x x x x x x x x x x x x x x x x x x x J r

  11. Solution

  12. Example 4 I What is the magnetic field inside and outside: A hollow copper pipe carrying current I?

  13. Example 5 I I What is the magnetic field inside and outside: A coaxial cable carrying equal currents (in opposite directions) on the inner and outer conductors?

  14. Solution

  15. Infinitely Long “Solenoid” (long straight coil/helix) Current I flows in each turn of the coil. The number of turns of wire per meter of solenoid is called the turn density n. I B inside the solenoid is uniform and has magnitude and is uniform.What is the direction of B?

  16. Field patterns for circular coils x x x x x Single Coil: B I Several Coils:

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