Final answer:
There seems to be an error in the question or the calculation process, as the computed value for sin(θ) exceeds 1, which is not possible. The formula for the magnetic force on a current-carrying wire is F = ILBsin(θ). The given values should be double-checked for accuracy and consistency.
Step-by-step explanation:
To find the angle between the wire and the magnetic field, we can use the formula for the magnetic force (F) acting on a segment of current-carrying wire, which is given by F = ILBsin(θ), where I is the current, L is the length of the wire, B is the magnetic field strength, and θ is the angle between the wire and the magnetic field.
We are given that the force (F) is 1.6 N, the current (I) is 3.1 A, the length of the wire (L) is 1.3 x 10-6 meters (since 1.3 μm is equal to 1.3 x 10-6 meters), and the magnetic field strength (B) is 0.51 T. Using the above formula, we can solve for θ:
1.6 = (3.1)(1.3 x 10-6)(0.51)sin(θ)
sin(θ) = 1.6 / (3.1)(1.3 x 10-6)(0.51)
sin(θ) = 1.6 / (2.0533 x 10-6)
sin(θ) = 779,124.21
Now taking the arcsine of both sides, we get:
θ = arcsin(779,124.21)
However, this value is clearly not possible, as the sin() of an angle cannot be greater than 1. There appears to be a mistake in the given values or the calculations. Please double-check the values and ensure they are consistent with typical orders of magnitude for such problems. Generally, the magnetic field strength (B) for schoolwork questions is on the order of 10-1 to 101 teslas, and typical current values (I) are on the order of 10-1 to 102 amperes. The provided values lead to an unrealistic computation, which may indicate the presence of a typographical or conceptual error in the question or a misunderstanding of the formula.