Magnitude of Torque on a current loop

[NikitaY]

Homework Statement

A small current loop of area A=0.0008m2 and moment of inertia I=6.9e-07kgm2 carries a current i=0.0039A with its magnetic moment perpendicular to the Earth's magnetic field. The magnitude of the Earth's field is B=4.2e-05T.

a). What is the magnitude of the net torque T on the loop?
T = ____ Nm

b). What is the angular acceleration a of the loop?
a = ___ rad/s2

Homework Equations

τ = NiABsinθ
α = τ/I

The Attempt at a Solution

I have the equation for toque and I am given all of the variables. I assumed that N = 1, and θ = 90°. When I plug in all of the numbers, I get the following:
τ = (1)*(.0039 A)*(.0008 m^2)*(4.2e-05 T)*sin90° = 1.3104*10-10 Nm. That is not the correct answer, however. I do not know what to do at this point. If I could get the torque, I would then be able to easily get the angular acceleration. Any help would be greatly appreciated. Thank you!

 

[anathema]

First, make sure that all of your units are consistent. In your calculation, you have the units of amperes (A), meters squared (m^2), and teslas (T). However, the unit for torque is newton-meters (Nm), so you need to convert the units of current and magnetic field to newtons and meters, respectively.

To do this, you can use the fact that 1 ampere = 1 newton/meter. So, the units for current will be N*m/(m^2*T), which simplifies to N/T. Similarly, the units for magnetic field will be N/(m^2*A), which simplifies to N/(A*m). Make sure to include these unit conversions in your calculation.

Also, the angle θ should be in radians, not degrees. So, instead of using sin90°, use sin(90°*π/180) or sin(π/2).

After making these corrections, you should get the correct answer for torque. To find the angular acceleration, simply divide the torque by the moment of inertia, which is given as 6.9e-07 kgm^2.

Hope this helps!