12.4 Ampère’s Law

Use Ampère’s law to describe the magnetic field created by a moving charge carrier.

• Ampère’s law relates the magnitude of the magnetic field to the current enclosed by a closed imaginary path called an Amperian loop. Relevant equation:
  • i. Ampère’s law can be used to determine the magnetic field near a long, straight currentcarrying wire. Derived equation:
  • ii. Unless otherwise stated, all solenoids are assumed to be very long, with uniform magnetic fields inside the solenoids and negligible magnetic fields outside the solenoids.
  • iii. Ampère’s law can be used to determine the magnetic field inside of a long solenoid. Derived equation: Bnsol0=µ I
• An Amperian loop is a closed path around a current-carrying conductor. TOPIC 12.4 Ampère’s Law
• The principle of superposition can be used to determine the net magnetic field at a point in space created by various combinations of current-carrying conductors, or conducting loops, segments, or cylinders.
• Maxwell’s equations are the collection of equations that fully describe electromagnetism. Maxwell’s fourth equation is Ampère’s law with Maxwell’s addition; it states that magnetic fields can be generated by electric current (Ampère’s law) and that a changing electric field creates a magnetic field, similar to the way a moving charge creates a magnetic field (Maxwell’s addition). Relevant equations: BOUNDARY STATEMENT AP Physics C: Electricity & Magnetism only expects quantitative application of Ampère’s law limited to situations involving symmetrical magnetic fields. Long straight wires, long solenoids carrying currents, as well as conductive slabs or cylindrical conductors carrying a current density, are the types of shapes to which Ampère’s law will be applied on the AP Physics C: Electricity & Magnetism Exam. BOUNDARY STATEMENT AP Physics C: Electricity & Magnetism does not expect students to use Maxwell’s fourth equation with a changing electric field. However, students should understand that a changing electric field generates a magnetic field.