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Force Between Two Parallel Wires:
Ampere’s Law:
Curl your right hand around the Amperian loop,
with the fingers pointing in the direction of
integration. A current through the loop in the
general direction of your outstretched thumb is
assigned a plus sign, and a current generally in
the opposite direction is assigned a minus sign.
Ampere’s Law, Magnetic Field Outside a Long Straight Wire
Carrying Current:
Ampere’s Law, Magnetic Field Inside a Long Straight Wire
Carrying Current:
Example, Ampere’s Law to find the magnetic field inside a long cylinder of
current.
Solenoids and Toroids:
Fig. 29-17 A vertical cross section through
the central axis of a “stretched-out”
solenoid. The back portions of five turns
are shown, as are the magnetic field lines
due to a current through the solenoid. Each
turn produces circular magnetic field lines
near itself. Near the solenoid’s axis, the
field lines combine into a net magnetic
field that is directed along the axis. The
closely spaced field lines there indicate a
strong magnetic field. Outside the solenoid
the field lines are widely spaced; the field
there is very weak.
Solenoids:
Fig. 29-19 Application of Ampere’s law to a section of a
long ideal solenoid carrying a current i. The Amperian
loop is the rectangle abcda.
Here n be the number of turns per unit length of the solenoid
Magnetic Field of a Toroid:
where i is the current in the toroid windings (and is positive for those windings
enclosed by the Amperian loop) and N is the total number of turns. This gives
Example, The field inside a solenoid:

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Ampere law

  • 1. Force Between Two Parallel Wires:
  • 2. Ampere’s Law: Curl your right hand around the Amperian loop, with the fingers pointing in the direction of integration. A current through the loop in the general direction of your outstretched thumb is assigned a plus sign, and a current generally in the opposite direction is assigned a minus sign.
  • 3. Ampere’s Law, Magnetic Field Outside a Long Straight Wire Carrying Current:
  • 4. Ampere’s Law, Magnetic Field Inside a Long Straight Wire Carrying Current:
  • 5. Example, Ampere’s Law to find the magnetic field inside a long cylinder of current.
  • 6. Solenoids and Toroids: Fig. 29-17 A vertical cross section through the central axis of a “stretched-out” solenoid. The back portions of five turns are shown, as are the magnetic field lines due to a current through the solenoid. Each turn produces circular magnetic field lines near itself. Near the solenoid’s axis, the field lines combine into a net magnetic field that is directed along the axis. The closely spaced field lines there indicate a strong magnetic field. Outside the solenoid the field lines are widely spaced; the field there is very weak.
  • 7. Solenoids: Fig. 29-19 Application of Ampere’s law to a section of a long ideal solenoid carrying a current i. The Amperian loop is the rectangle abcda. Here n be the number of turns per unit length of the solenoid
  • 8. Magnetic Field of a Toroid: where i is the current in the toroid windings (and is positive for those windings enclosed by the Amperian loop) and N is the total number of turns. This gives
  • 9. Example, The field inside a solenoid: