1. Day 5: General Form of Faraday’s Law How a changing magnetic Flux Produces an Electric Field Example of an E-Field is produced by a changing B-Field The General form of Faraday’s Law The Electrostatic (Coulombic) Force vs. the Induced Electric Force

2. A Changing Flux Produces an Electric Field When a current flows through a wire, there is an electric field in the wire that does the work of moving the electrons in the wire The current moving through the wire produces a magnetic field Conversely, a changing magnetic flux induces a current in the wire which implies there is an electric field induced in the wire by the magnetic flux

3. A changing Magnetic Flux Produces an Electric Field E-Field moving the current Induced E-Field a The EMF induced in this circuit is equal dl to the work done per unit charge by the electric field around a closed path b

4. The General Form of Faraday’s Law The integral is taken around a closed path enclosing the area through which the magnetic flux Φ B is changing This is a more elegant statement of Faraday’s Law and is valid not only in conductors but in any region of space

5. E-Field Produced by a Changing B-Field Inside the magnet (r < r 0 ) Outside the magnet (r > r 0 )

6. E-Field Produced by a Changing B- Field Inside the magnet, the electric field increases linearly from zero (at the center) to at the edge Outside the magnet, the electric field decreases inversely with the radial distance, beyond the edge of the magnetic field

7. The Electrostatic Force is a Conservative Force The general form of faraday’s law is a closed path integral, and the electric field produced by electric charges at rest (electrostatic field) yields: If the path is closed, then points a & b are the same points and: because these points are at the same potential (ΔV a-a =0) This follows from the fact that the electrostatic (Coulombic) force is a conservative force and that the work done per unit charge around any closed path = 0 & is independent of the path taken

8. The Non-static Electric Force is a non- Conservative Force But in the non-electrostatic case when the electric field is produced (induced) by a changing magnetic field, then the closed integral is not zero. Therefore, the conclusion is that the forces resulting from the changing magnetic fields are non-conservative and the induced electric field is a non-conservative field !