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AP Physics C: Electricity & Magnetism 12.4 Amp Res Law Questions

Apply Ampere's law to symmetric current distributions and use enclosed current, superposition, graphs, and experiments to analyse magnetic fields.

Syllabus
Effective Fall 2024
Course
AP Physics C: Electricity & Magnetism

Exam points

  • select an Amperian loop whose field direction and magnitude follow the source symmetry
  • relate the field line integral to the signed current enclosed by the chosen path
  • derive fields for long wires, solid or hollow conductors, coaxial cables, and solenoids
  • integrate current density and construct piecewise field expressions across radial regions
  • superpose long-wire fields and determine locations or regions where the net field vanishes

Covered syllabus points

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

Question 1

[Maximum number: 3]

Long, parallel wires S and T are a distance 2 d apart. Both wires carry equal currents I, but the currents are in opposite directions. Both wires are parallel to the x-axis. At the instant shown in Figure 1, Sphere 1 is a distance d above Wire S, Sphere 2 is a distance d below Wire S, and both spheres are moving with speed v in the +x-direction. Each sphere has positive charge +Q.

Gravitational effects are negligible.

Figure 1

Figure 1

Derive an expression for the magnitude Btot B_{\text {tot }} of the magnetic field at the location of Sphere 2 due to the currents in wires S and T in terms of d, I, and physical constants, as appropriate.

Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

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