# 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.

## Part 1#

Path A:

• $$-3\mu_0 I$$

• $$-\mu_0 I$$

• zero

• $$\mu_0 I$$

• $$3\mu_0 I$$

## Part 2#

Path B:

• $$-4\mu_0 I$$

• $$-2\mu_0 I$$

• zero

• $$2\mu_0 I$$

• $$4\mu_0 I$$

## Part 3#

Path C:

• $$-7\mu_0 I$$

• $$-\mu_0 I$$

• zero

• $$\mu_0 I$$

• $$7\mu_0 I$$

## Part 4#

Path D:

• $$-2\mu_0 I$$

• $$-\mu_0 I$$

• zero

• $$\mu_0 I$$

• $$2\mu_0 I$$