Answer:
The magnetic field inside a solenoid can be calculated using the formula:
B = μ₀nI
where B is the magnetic field, μ₀ is the permeability of free space (4π × 10^-7 T·m/A), n is the number of turns per unit length, and I is the current.
In this case, we can rearrange the formula to solve for n:
n = B/(μ₀I)
Plugging in the given values, we get:
n = (4.5 T)/(4π × 10^-7 T·m/A × 80 A)
n ≈ 1773 turns/m
Since the solenoid has a length of 0.64 m, the total number of turns is:
N = nL = 1773 turns/m × 0.64 m
N ≈ 1133 turns
Therefore, the solenoid has approximately 1133 turns