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Ampere’s Law

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

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Ampere’s Law

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  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. ds ´ I Ampere’s Law B • 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

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

  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 ℓsides (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

  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

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