1. Ampere’s Law AP Physics C Mrs. Coyle Andre Ampere

2. Remember: Biot-Savart Law: Field produced by current carrying wires –Distance a from long straight wire –Centre of a wire loop radius R –Centre of a Solenoid with N turns

3. Remember: There are two ways to find the electric field around a charged object. Coulomb’s Law (Superposition) Gauss’s Law This is used for high symmetry cases.

4. There are two ways to calculate magnetic field. Biot-Savart Law Ampere’s Law –Used for high symmetry cases.

5. Ampere’s Law For small length elements ds on a closed path (not necessarily circular) I is enclosed current passing through any surface bounded by the closed path. Note: dot product Use where there is high symmetry  ds I B

6. Sign Convention for the Current in Ampere’s Law r The current I passing through a loop is positive if the direction of B from the right hand rule is the same as the direction of the integration (ds). r positive I I B ds I B negative I

7. Field Outside a Long Straight Wire at a distance r from the center, r > R The current is uniformly distributed through the cross section of the wire

8. Field Inside a Long Straight Wire at a distance r from the center, r< R Inside the wire, the current considered is inside the amperian circle Note the linear relationship of B with r

9. Field Due to a Long Straight Wire The field is proportional to r inside the wire The field varies as 1/r outside the wire Both equations are equal at r = R

10. Magnetic Field of a Toroid Find the field at a point at distance r from the center of the toroid The toroid has N turns of wire

11. Magnetic Field of an Thin Infinite Sheet Rectangular amperian surface The w sides of the rectangle do not contribute to the field The two ℓ sides (parallel to the surface) contribute to the field J s =I/ l is the linear current density along the z direction The current is in the y direction

12. Magnetic Field of a Solenoid The field lines in the interior are –approximately parallel to each other –uniformly distributed –close together The field is strong and almost uniform in the interior

13. Magnetic Field of a Tightly Wound Solenoid The field distribution is similar to that of a bar magnet As the length of the solenoid increases –the interior field becomes more uniform –the exterior field becomes weaker

14. Ideal Solenoid –The turns are closely spaced –The length is much greater than the radius of the turns

15. Magnetic Field Inside a Long Solenoid -The total current through the rectangular path equals the current through each turn multiplied by the number of turns

16. Note The magnetic field inside a long solenoid does not depend on the position inside the solenoid (if end effects are neglected).

17. Magnetic Field –At a distance a from long straight wire –At the centre of a wire loop radius R –At the centre of a solenoid with N turns -In the interior of a toroid