Question

The units of torque (N⋅m) can be verified as equivalent to the units of A⋅m²T through the equation τ=NIABsinθ.

a) N⋅m = A⋅m²T
b) N⋅m ≠ A⋅m²T
c) N⋅m ≈ A⋅m²T
d) N⋅m > A⋅m²T

Answer 1

The units of torque (N·m) are equivalent to the units of A·m²T when analyzing the torque on a current-carrying loop in a magnetic field, as per the formula T = NIAB sin θ.

Step-by-step explanation:

Since the equation for torque on a current-carrying loop is T = NIAB sin θ, where T is torque, N is the number of turns in the loop, I is the current, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the perpendicular to the loop's plane and the magnetic field, the units of torque must be verifiable.

The SI unit of torque is newtons times meters (N·m), which can be verified to be equivalent to the units of ampere times meters squared times tesla (A·m²T), given that newton (N) is the SI unit of force and is defined as kg·m/s². Substituting the units from the formula T = NIAB sin θ, you get units of (A)(m)(m)(T), which simplify to A·m²T. Thus, the units of torque, N·m, are equivalent to A·m²T, and option (a) N·m = A·m²T is correct.