Flux through a loop

Flux through a loop#

Evaluate the magnetic flux \(\oint\vec{\mathbf{B}}\cdot d\vec{\mathbf{\ell}}\) for each of the cases shown in the figure.

Various Amperian loops threaded by currents

Part 1#

Part (a):

Answer Section#

  • \(-2\mu_0\)

  • \(-\mu_0\)

  • zero

  • \(\mu_0\)

  • \(2\mu_0\)

Part 2#

Part (b):

Answer Section#

  • \(-11\mu_0\)

  • \(-9\mu_0\)

  • zero

  • \(9\mu_0\)

  • \(11\mu_0\)

Part 3#

Part (c):

Answer Section#

  • \(-5\mu_0\)

  • \(-1\mu_0\)

  • zero

  • \(\mu_0\)

  • \(5\mu_0\)

Part 4#

Part (d):

Answer Section#

  • \(-6\mu_0\)

  • \(-2\mu_0\)

  • zero

  • \(2\mu_0\)

  • \(6\mu_0\)

Part 5#

Part (e):

Answer Section#

  • \(-11\mu_0\)

  • \(-5\mu_0\)

  • zero

  • \(5\mu_0\)

  • \(11\mu_0\)

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.