Question

a counterclockwise current of 3.0 a is circling around a wire loop (positioned directly in front of you) having an area of 5.8×10^(-2) m². what is the magnetic dipole moment?
52 a/m², oriented directly away from you
52 a/m², oriented directly towards you
0.17 a·m², oriented directly away from you
0.17 a·m², oriented directly towards you
none of the choices are correct.

Explanation:

Step1: Recall magnetic - dipole moment formula

The formula for the magnetic - dipole moment of a current - carrying loop is $\mu = IA$, where $I$ is the current and $A$ is the area of the loop.

Step2: Substitute given values

Given $I = 3.0\ A$ and $A=5.8\times 10^{-2}\ m^{2}$. Then $\mu=(3.0\ A)\times(5.8\times 10^{-2}\ m^{2}) = 0.174\ A\cdot m^{2}\approx0.17\ A\cdot m^{2}$.

Step3: Determine the direction

Using the right - hand rule, for a counter - clockwise current as seen from the front, the magnetic dipole moment is directed towards you.

Answer:

0.17 A $\cdot$ m$^{2}$, oriented directly towards you