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