Amperes Law

What is Amperes Law

• it’s a much easier version of Biot-Savart Law as it’s not only simpler but more concise

• Formula

  • $\int \vec{B}\cdot d\vec{l}={\mu }_0{I}_{enclosed}$

    • what does this mean?

      • B is the magnetic field in the “amperian” loop we chose

      • dl is the dl of the amperian loop so

        • so if it’s a circle we would use $2\pi r$

      • $I_{enclosed}$ is the current enclosed in the amperian loop

• NOTE!!!

  • this only works if B is uniform in the amperian loop

Solid wire carrying uniform current I

• 

  • r < R

    • $B(2\pi r)={\mu }_0\left(\frac{I}{\pi R^2}\right)(\pi r^2)$

  • r > R

    • $B(2\pi r)={\mu }_{0}I$

Hollow wire with uniform current I

• 

  • r < a

    • B = 0

  • a < r < b

    • $B(2\pi r)={\mu }_0\left(\frac{I}{\pi b^2-\pi a^2}\right)(\pi r^2-\pi a^2)$

  • r > b

    • $B(2\pi r)={\mu }_{0}I$