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

2. Example 1: Long parallel wires Find force on current I 1 in segment ab due to current I 2 (magnitude & direction) L I1I1 d (Take I 1 = 20A, I 2 =30A, d=0.01m, L=1.5m) a b I2I2

3. Solution

4. Quiz I1I1 I2I2 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) Left B) Right C) Rotate clockwise D) Rotate counter-clockwise E) It won’t move

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

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: i)use symmetry to choose an appropriate path ii)determine the direction of B from RHR. iii)calculate (in terms of |B|) iv)calculate I encircled v)apply Ampere’s Law to get B Ampere’s Law holds only for steady currents

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

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. B ds path of integration field line I Solution

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

11. Solution

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

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

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 Single Coil: I B Several Coils: xxxxx