Final answer:
The magnetic field at the center of a solenoid with 54 turns per centimeter, a radius of 1.11 cm, and a current of 0.160 A can be calculated using the formula B = μ0 * n * I, resulting in a magnetic field of 0.136 T.
Step-by-step explanation:
To calculate the magnetic field at the center of a solenoid, we can use Ampère's Law which simplifies to the formula B = μ0 * n * I where B is the magnetic field, μ0 is the magnetic constant (4π x 10-7 T·m/A), n is the number of turns per unit length of the solenoid, and I is the current. In your case, we have a solenoid with 54 turns per centimeter (which we convert to 5400 turns per meter), a current of 0.160 A, and because we're working in air, μ0 is still 4π x 10-7 T·m/A.
The calculation would look like this:
First, convert turns per centimeter to turns per meter: 54 turns/cm * 100 cm/m = 5400 turns/m
Then, plug the values into the formula:
B = (4π x 10-7 T·m/A) * (5400 turns/m) * (0.160 A)
Solve for B:
B = 0.136 T or 136 mT (milliteslas)
Thus, the magnetic field at the center of the solenoid is 0.136 T.