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AP Physics C E and M 12.4: Ampère’s Law

Apply Ampère’s law to relate magnetic circulation around a closed path to the current enclosed by that path, using symmetry when appropriate.

Syllabus
Effective Fall 2025
Course
AP Physics C: Electricity & Magnetism

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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