Final answer:
To generate a 10 T magnetic field with a solenoid that has 2000 turns per meter, the required current is calculated using the formula B = μ_0 n I, resulting in a required current of approximately 3981.07 A.
Step-by-step explanation:
To design a superconducting solenoid that generates a magnetic field of 10 T (teslas), we need to calculate the current required for a solenoid with a given number of turns per meter. The magnetic field B inside a long solenoid is given by the formula B = μ_0 n I, where μ_0 is the permeability of free space (1.2566370614 × 10-6 T·m/A), n is the number of turns per meter, and I is the current in amperes.
In this case, the solenoid has 2000 turns per meter and we wish to generate 10 T. Plugging in the values, we get:
10 T = (1.2566370614 × 10-6 T·m/A) × 2000 turns/m × I
Solving for I, we find:
I = 10 T / ((1.2566370614 × 10-6 T·m/A) × 2000 turns/m)
Therefore, the required current is I = 3981.07 A (rounded to two decimal places). Thus, to generate a 10 T magnetic field with a solenoid that has 2000 turns per meter, a current of approximately 3981.07 A would be needed.