# Ampere’s Law

We just need a closed loop. We don’t need a closed surface like we needed to apply Gauss Law. $∮_{C}B⋅dl=μ_{0}I_{enc}=μ_{0}∫_{S}J⋅dS$

Use the right hand rule and curl your fingers around the loop. Your thumb will be pointing in the positive current direction.

You can definitely make a parallel to Gauss Law. Same thing with $Q_{encl}$ but for $I_{encl}$

### Calculations Steps to find Magnetic Field

Making parallels with Gauss Law to find Electric Field, but Ampere’s Law is much less strict. → Ex: See how it is used in Solenoid?

We need to remember that the loop is a 2D structure. So we have to see how current is flowing to take a cross-section perpendicular to the current. On this plane, we look for symmetry and think of a loop where $B$ would be constant.

##### Steps

- Identify symmetry, sketch magnetic field lines
- Draw or define a proper Amperian loop to evaluate $∮B⋅dl$
- Make sure that $B$ is always parallel or perpendicular to $dl$ so that you can factor $B$ out

- Rearrange and solve for $∣B∣$
- Determine the direction of $B$ in final answer

Practical application: use of a Clamp Meter