The Magnetic Dipole Moment — Question 1

Question 1

Current sense determines the magnetic moment before torque and energy are calculated

A 40-turn circular coil of radius .0250 m carries .200 A clockwise when viewed from +z. The external field is $(.300\hat x+.400\hat z)$ T. Define dipole potential energy to be zero when the moment is perpendicular to the field.

1. Find the magnetic-moment vector.

2. Find the torque vector and potential energy.

Question 1 - Solution

Current sense determines the magnetic moment before torque and energy are calculated

(a) Method and calculation

$$\mu=NIA=(40)(.200)\pi(.0250)^2=.00500\pi\,\mathrm{A\,m^2}.$$$$\vec\mu=-.00500\pi\hat z\,\mathrm{A\,m^2}\quad\text{by the current right-hand rule}.$$

(b) Interpretation and further calculation

$$\vec\tau=\vec\mu\times\vec B=-.00150\pi\hat y\,\mathrm{N\,m}.$$$$U=-\vec\mu\cdot\vec B=+.00200\pi\,\mathrm J.$$

Physical check

A positive potential energy here means the moment has a component opposite to the applied field.