2. Physics 223

3. 30. Sources of the Magnetic Field 30.1 Biot-Savart Law 30.2 Force between two parallel wires 30.3 Ampere’s Law 30.4 Magnetic Field (B) of a Solenoid 30.5 Gauss’s Law in Magnetism

4. Biot-Savart Law B= μ 0 I / 4π ∫ (d  s x r ̂ ) / r 2

5. Electric Currents Produce Magnetism I I B = μ 0 I / 2 a a

6. Electric Currents Produce Magnetism Right Hand Rule: Thumb points to B and curled fingers indicate I I I B

7. Electric Currents Produce Magnetism B = μ 0 I a 2 / 2( a 2 + x 2 ) 3/2 B x a

8. Electric Currents Produce Magnetism Right-Hand Rule: Thumb points to current ( I) and curled fingers indicate B I B B

9. Electric Currents Produce Magnetism Old wine … New bottle! I X

10. B of Infinitely-Long Wire I B B B =  o I / 2  a

11. B of Finite-Length Wire I B B B =  o I [sin θ 1 - sin θ 2 ] / 4  a

12. 30.2 Force Between Two Currents F =  o I 1 I 2 L / 2  a I1I1 I2I2

13. 30.3 Ampere’s Law ∫B. ds =  0 I I B B

14. 30.4 B of a Solenoid Application of Ampere’s Law ∫B. ds =  0 I B L =  0 N I B =  0 N I /L B =  0 n I L

15. 30.5 Gauss’s Law in Magnetism ∫B. dA =  B

16. Flux Through the Rectangular Loop  B =  0 I b/2  ln(1 + a/c) I X c a b

17. That’s all folks!