You measure the magnetic field of a long, current-carrying wire to be B is equal to start fraction 50 times mu naught over pi end fraction at a distance of r = 7.5 cm. How much current is running through the wire?

  I = 1.875 A

Explanation:

For this exercise we use Ampere's law

             ∫ B . ds = μ₀  I

We use a circular path around the wire whereby B and ds are parallel, whereby the dot product is reduced to the algebraic product

               ds = 2π dr

               B (2πr) = μ₀  I

              I = B 2π R /μ₀  

              r= 7.5 cm = 0.075 m

calculate

             I = (50 μ₀ /π) 2π 0.075 /μ₀  

             I = 1.875 A

the force on the thing and the distance the force moves the thing