Flux due to a coil

Flux due to a coil#

The coil whose lengthwise cross section is shown in the figure carries a current \(I\) and has \(N\) evenly-spaced turns distributed along the length \(\ell\). Evaluate the magnetic flux \(\oint\vec{\mathbf{B}}\cdot d\vec{\mathbf{\ell}}\) for each of the paths indicated.

The cross section of a coil with various Amperian loops

Part 1#

Path A:

Answer Section#

  • \(-3\mu_0 I\)

  • \(-\mu_0 I\)

  • zero

  • \(\mu_0 I\)

  • \(3\mu_0 I\)

Part 2#

Path B:

Answer Section#

  • \(-4\mu_0 I\)

  • \(-2\mu_0 I\)

  • zero

  • \(2\mu_0 I\)

  • \(4\mu_0 I\)

Part 3#

Path C:

Answer Section#

  • \(-7\mu_0 I\)

  • \(-\mu_0 I\)

  • zero

  • \(\mu_0 I\)

  • \(7\mu_0 I\)

Part 4#

Path D:

Answer Section#

  • \(-2\mu_0 I\)

  • \(-\mu_0 I\)

  • zero

  • \(\mu_0 I\)

  • \(2\mu_0 I\)

Attribution#

Problem is from the OpenStax University Physics Volume 2 textbook, licensed under the CC-BY 4.0 license.
Image representing the Creative Commons 4.0 BY license.