Final answer:
The magnetic field inside the solenoid is calculated using the formula B = μ0nI, resulting in a magnetic field strength for the given solenoid specs.
Step-by-step explanation:
To calculate the magnetic field inside a solenoid we can use the formula B = μ0nI, where B is the magnetic field, μ0 is the permeability of free space (μ0 = 4π x 10-7 T·m/A), n is the number of turns per unit length of the solenoid, and I is the current. For a solenoid with 200 loops and a length of 50 cm (0.5 m), first, we find n by dividing the number of loops by the length of the solenoid in meters (n = 200 / 0.5 m = 400 turns/m). Then we multiply this value by the permeability of free space and the current (4.2 A) to find the magnetic field. As a result, the magnetic field B within the solenoid is given by B = 4π x 10-7 T·m/A x 400 turns/m x 4.2 A.