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

• oogleshmoogle
In summary, the use of Ampere's law requires symmetry in the integral around the loop, such as in cases of radial or linear symmetry. However, for non-symmetric cases like a single circular current carrying loop, the Biot-Savart law must be used instead. While both can be used to solve these cases, the Biot-Savart law integrals are more challenging.

#### oogleshmoogle

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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.

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