Suppose that we can use wire of \(1.0-\mathrm{mm}\) diameter to make either a single loop of wire or a solenoid, and we wish to compare, for a given current, the magnetic fields at the center of each.

(a) Use the Biot-Savart law to derive an expression for the magnetic field magnitude at the center of a circular current loop.

(b) Compare the magnitude of the magnetic field at the center of a circular current loop of radius \(10 \mathrm{~mm}\) with the magnitude of the magnetic field at the center of a solenoid of the same radius and with 1. 0 turn per millimeter. Assume the current is the same through the current loop and the solenoid.