Final answer:
To calculate the magnetic field at the center of the coil, the formula B = μ0 * (N * I) / (2 * R) is used, inserting the provided values of radius, number of turns, and current.
Step-by-step explanation:
To calculate the magnetic field at the center of a coil, we can use Ampère's Law, which relates magnetic fields to the electric currents that produce them. Specifically, for a solenoid or a coil of wire, the magnetic field (B) at the center is given by the formula B = μ0 * (N * I) / (2 * R), where μ0 is the magnetic constant (also known as the permeability of free space), N is the number of turns in the coil, I is the current through the coil, and R is the radius of the coil.
Using the information provided, with a radius R of 10 cm (0.1 meters), 100 turns of wire (N = 100), and a current (I) of 0.5 A, we can substitute these values into the formula to get B = (4π x 10^{-7} T*m/A) * (100 * 0.5 A) / (2 * 0.1 m). Thus, calculating this will provide us with the magnetic field at the center of the coil.