Final answer:
The magnetic dipole moment of a circular loop of wire with a radius of 20 cm and current of 2 A, is the product of the current and the area of the loop, which calculates to 0.25π A·m^2. As the current flows counterclockwise when viewed from above, the direction of the moment is in the positive z-axis. The closest option provided in the question is 0.25 A·m^2, in the positive z direction.
Step-by-step explanation:
The magnetic dipole moment for a circular loop of wire is given by the product of the current I and the area A of the loop. In mathematical form, it is μ = IA, where I is the current and A is the area of the loop. To find the area A of the loop, we use the formula for the area of a circle, which is A = πr^2, where r is the radius of the loop.
For a loop with a radius of 20 cm (or 0.2 meters), the area A is π(0.2 m)^2, and the current I is 2 A. Thus, the magnetic dipole moment μ is (2 A)(π)(0.2 m)^2, which results in μ = 0.25π A·m^2.
Since the current is flowing counterclockwise when viewed from the positive z-axis, by the right-hand rule, the magnetic dipole moment is in the positive z-direction. Therefore, the correct answer is:
(c) 0.25π A·m^2, in the positive z direction, but considering π as part of the calculation and given that the options do not include π, the closest to the numerical value calculated would be:
(a) 0.25 A·m^2, in the positive z direction.