Final answer:
The maximum torque that can act on a 131.0 cm wire loop carrying a current of 0.80 A in a magnetic field of 0.50 T is approximately 0.05468 N·m. This calculation assumes that the wire is formed into a single circular loop and that the plane of the loop is perpendicular to the magnetic field.
Step-by-step explanation:
To find the maximum torque that can act on a wire loop in a magnetic field, one can use the formula τ = nIABsinθ, where τ is torque, n is the number of turns, I is the current, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the plane of the loop and the direction of the magnetic field. For a single circular loop, n is 1, and the sine of the angle between the plane of the loop and the field direction is 1 when they are perpendicular to each other for the maximum torque. Given the information provided, the wire will create a circle with a circumference of 131.0 cm, which allows us to calculate the radius and, consequently, the area A for the loop.
The circumference of a circle is given by C = 2πr, where r is the radius. If the circumference is 131.0 cm, we can find the radius r as follows:
r = C / (2π) = 131.0 cm / (2π) ≈ 20.84 cm
Now, converting the radius to meters:
r = 20.84 cm * (1 m / 100 cm) = 0.2084 m
To find the area A of the loop:
A = πr² = π (0.2084 m)² ≈ 0.1367 m²
Now we can calculate the maximum torque knowing that sinθ = 1 (maximum torque occurs when the plane of the loop is perpendicular to the magnetic field):
τ = nIABsinθ = (1) (0.80 A) (0.1367 m²) (0.50 T) (1) = 0.05468 N·m
Therefore, the maximum torque on the loop is approximately 0.05468 N·m when the loop is perpendicular to the magnetic field.