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

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

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

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

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!

Peer criticism MAXWELL HEAVISIDE

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

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

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

Example: current sheet