1. Christopher Crawford PHY 311 2014-03-31
§5.2: Biot-Savart Law
Christopher Crawford
PHY 311

2. Outline Review Ampère’s parallel wire force law Current elements
Biot-Savart law
Ampère’s generalization to arbitrary loop
Correction and equivalence with Biot-Savart law
Examples
Straight wire
Circular loop
Current sheet

3. Review: Magnetic force – straight wires
Andre Marie Ampere shows that parallel currents attract and antiparallel currents repel
We want to generalize this to any currents similar to the Coulomb force

4. Current elements Analogous to charge elements – different dimensions
Relations between charge / current and different dimensions – analogy: multi-lane highway – current flux
Lorentz force

5. Ampère’s generalization
Experimental laws:
Force formula
Problem
The force between two current elements does NOT point along the line from the one to the other!

6. Peer criticism
MAXWELL
HEAVISIDE

7. Biot-Savart Law Coulomb’s Law Biot-Savart Law
Consistency of separation of force into: I’dl’ –> B –> I dl

8. Example 5.5: straight wire
Similar to Ch. 2: line charge

9. Example 5.6: dipole loop
Closest thing to an electric point charge

10. Example: current sheet