All questions
AP Physics C: E&M
12.4 Ampère’s Law
IntermediateMCQMathematicalConceptual25.7k
A top-down view shows four circular wire cross-sections arranged horizontally in a plane. From left to right: the first circle contains a central black dot and is labeled \(3I_0\); the second circle contains an interior cross and is labeled \(I_0\); the third circle contains an interior cross and is labeled \(2I_0\); the fourth circle contains a central black dot and is labeled \(2I_0\). Three distinct closed loops surround subsets of these wires. A solid oval loop labeled \(C_1\) encloses the first and second circles, with a single counterclockwise arrowhead on its top boundary. A dashed oval loop labeled \(C_2\) encloses the second, third, and fourth circles, with a single counterclockwise arrowhead on its top boundary. A dotted oval loop labeled \(C_3\) encloses the first, second, and third circles, with a single counterclockwise arrowhead on its bottom boundary. No other labels, lines, text, or axes appear.
Four parallel current-carrying wires and three closed integration paths oriented counterclockwise.
Four long, straight parallel wires perpendicular to the page carry steady currents: Wire 1 carries current \(3I_0\) directed out of the page, Wire 2 carries current \(I_0\) directed into the page, Wire 3 carries current \(2I_0\) directed into the page, and Wire 4 carries current \(2I_0\) directed out of the page.

Three closed paths lie in the plane of the page and are each traversed counterclockwise: path \(C_1\) encloses only Wires 1 and 2, path \(C_2\) encloses only Wires 2, 3, and 4, and path \(C_3\) encloses only Wires 1, 2, and 3.

Which row in the table correctly identifies the value of the line integral \(\oint \vec{B} \cdot d\vec{\ell}\) along each path?

Path \(C_1\)Path \(C_2\)Path \(C_3\)
Row A\(-2\mu_0 I_0\)\(+\mu_0 I_0\)\(0\)
Row B\(+2\mu_0 I_0\)\(-\mu_0 I_0\)\(0\)
Row C\(+4\mu_0 I_0\)\(+5\mu_0 I_0\)\(+6\mu_0 I_0\)
Row D\(+2\mu_0 I_0\)\(-\mu_0 I_0\)\(+2\mu_0 I_0\)

Log In to Continue

Accounts are free! Log in to try this question, see explanations, save progress, and more!

Similar Questions

Tools for a 5

The Quiz Lab library of AP Physics quizzes AP aligned mock tests to help you get a 5. With grading, adaptive explanations, and more. Find a Quiz Find, solve, and grade every AP FRQ ever. Find an FRQ Stuck on AP Physics C: E&M? Get unstuck with an AP specialist.1 to 1 tutors who know the exam inside out. Understand weeks of material in a single session.Find a Tutor Learn AP Physics from scratch, quickly. This is the only course you'll need for the year. A self-paced course with everything you need to get a 5. Trusted by over 15,000 students and 200+ schools. Learn fast, or we'll refund your purchase, backed by our 100% satisfaction guarantee. Explore the Course