Amperes Law Andre Ampere AP Physics C Mrs

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

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

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.

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

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 B ds ´ I

Sign Convention for the Current in Ampere’s Law I I negative I positive I B r ds B ds 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).

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

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

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

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

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 • Js =I/l is the linear current density along the z direction • The current is in the y direction

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

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

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

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

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

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