When do I use Biot-Savart Law vs. Ampere's Law?

[oogleshmoogle]

This isn't a homework problem, I have the solutions for this problem. I'm just wondering why, for question 3, letter a, part ii, it's necessary to use the Biot-Savart law instead of Ampere's law? What are the use cases for Biot-Savart law vs. Ampere's law?

http://apcentral.collegeboard.com/apc/public/repository/ap08_physics_c_em_frq.pdf

 

[Charles Link]

In order to use Ampere's law, it is necessary to have some symmetry to the integral around the loop. i.e. for $\oint B \cdot dl=\mu_o I$ , in a problem with radial symmetry,(such as a long straight current carrying conductor), the $B$ is normally constant throughout the entire circular path that is chosen for the integral. For a linear symmetry, such as a long solenoid, a path of a thin rectangular loop is used. The $B$ is assumed to be zero outside the solenoid (over the outer part of the path) and the $B$ is assumed to have the same value on the entire length of the interior. Biot-Savart can also be used to solve these cases, but the Biot-Savart integrals are more difficult than the Ampere's law integrals. Meanwhile for a single circular current carrying loop, you don't have a symmetric path to use Ampere's law, and the Biot-Savart solution is necessary.

 

[oogleshmoogle]

Perfect answer, thank you so much! That totally clears me up.