How Is Torque Calculated on a Current Loop in a Magnetic Field?

[Alouette]

1. A small current loop of area A=0.0007m2 and moment of inertia I=6.6e-07kgm2 carries a current i=0.0045A with its magnetic moment perpendicular to the Earth's magnetic field. The magnitude of the Earth's field is B=4.2e-05T.

What is the magnitude of the net torque T on the loop?

Homework Equations

(1) τ(torque) = I($\alpha$

(2) τ = μ X B

(3) torque = current*area*B

The Attempt at a Solution

I'm not sure where to begin. I would plug numbers into the third equation but it doesn't make sense of where the moment of inertia comes into play...help?

edit:
Okay so I did use (3) to find the right answer. I'm not sure how this works though. so in my drawing i just have a square loop and the question says it is perpendicular to Earth's B field, I thought perpendicular meant they cancel out?

 

[tiny-tim]

Hi Alouette!

… with its magnetic moment perpendicular to the Earth's magnetic field.
…
(2) τ = μ X B
…
… i just have a square loop and the question says it is perpendicular to Earth's B field, I thought perpendicular meant they cancel out?

no, the question says that the magnetic moment (not the loop itself) is perpendicular to Earth's magnetic field

magnetic moment, µ, is a vector, current times area (amp-turns m²), and it points perpendicular to the loop

the H field is the magnetic moment density (amp-turns/m), which eg points along the axis of a solenoid, ie perpendicular to the loops