The magnitude of the magnetic field 50 centimetres from a long, thin, straight wire is 8.0 microteslas. What is the current through the long wire?
We can call the distance between the wire and the measured field value, 50 centimetres, 𝑑. And the magnitude of the magnetic field 8.0 microteslas we’ll name 𝐵. We want to solve for the current that runs through the long wire. We’ll call that current 𝐼.
There is a mathematical relationship that connects magnetic field 𝐵 from a long straight wire with the current that runs through that wire. This relationship says that the magnetic field 𝐵 is equal to 𝜇 nought, the permeability of free space, over two 𝜋 times the current 𝐼 divided by the distance from the wire that the field 𝐵 is measured. We’ll assume that the constant 𝜇 nought is equal to exactly 1.26 times 10 to the negative six tesla metres per amps.
We can rearrange this expression to solve for 𝐼, the current. We see that 𝐼 is equal to two 𝜋 times the distance 𝑑 multiplied by the magnetic field 𝐵 over 𝜇 nought. When we plug in for these values to solve for 𝐼, we’re careful to write our distance in units of metres and our magnetic field in units of teslas.
When we enter all these values on our calculator, we find that to two significant figures 𝐼 the current is 20 amps. That’s the magnitude of the current running through the long wire.