AP Physics C E and M 12.4 Ampere's Law

[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

Derive an expression for the magnitude $B_{\text {tot }}$ 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.

\multirow[t]{4}{*}{B} &

For a multistep derivation that includes the equation $\oint \vec{B} \cdot d \vec{\ell}=\mu_{0} I_{\text {enc }}$ or $d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I(d \vec{\ell} \times \hat{r})}{r^{2}}$
Scoring Note: Vector notation is not required for this point to be earned. A multistep derivation that includes $B=\frac{\mu_{0} I}{2 \pi d}$ can earn this point.

& Point B1 \\ \hline & For a correct expression for the magnitude of the magnetic field due to the current in one wire at the location of Sphere 2 & Point B2 \\ \hline & For indicating that the magnitude of the total field is twice that due to one wire & Point B3 \\ \hline &

Example Response
Determine the magnitude B of the magnetic field due to one wire. $\oint \vec{B} \cdot d \vec{\ell}=\mu_{0} I_{\mathrm{enc}}$ $\begin{aligned} & B(2 \pi d)=\mu_{0} I & B=\frac{\mu_{0} I}{2 \pi d} \end{aligned}$
Determine $B_{\text {tot }}$ . $\begin{aligned} & B_{\text {tot }}=\frac{\mu_{0} I}{2 \pi d}+\frac{\mu_{0} I}{2 \pi d} & B_{\text {tot }}=\frac{\mu_{0} I}{\pi d} \end{aligned}$

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AP Physics C: Electricity & Magnetism 12.4 A Use Amp Res Law to Describe the Magnetic Field Created By a Moving Charge Carrier Questions

Exam points

AP Physics C: Electricity & Magnetism 12.4 A Use Amp Res Law to Describe the Magnetic Field Created By a Moving Charge Carrier Questions question 1