Calculating Torque & Angular Acceleration of a Current Loop

[ibaraku]

Homework Statement

A small current loop of area A = 1.5cm^2 carries current I = 3.6mA. What torque acts on it in a lab where its magnetic moment is perpendicualr to the Earth's magnetic field of
4.2 x 10^-5
(b) Find its angular acceleration if its rotational inertia about a diameter is 6.2gcm^2

Homework Equations

T = m x B
m = IA

The Attempt at a Solution

I know that m = (.015)(.0036) = 5.4 * 10^-5.

T = abs(5.4 * 10^-5) * abs(B) * Sin(PI/2)

I'm a bit confused about what B is, should I use the B for Earth's magnetic field?

 

[Redbelly98]

Yes, use the given B for the Earth's magnetic field.

 

[thomate1]

If so, is it in the same direction as the magnetic moment of the current loop? Also, for the second part, I'm not sure how to incorporate the rotational inertia into the equation for angular acceleration.

I would approach this problem by first clarifying any uncertainties or questions about the given information. In this case, I would confirm with the instructor or the source of the problem what is meant by "perpendicular to the Earth's magnetic field". I would also ask for the direction of the Earth's magnetic field and how it relates to the magnetic moment of the current loop.

Assuming that the magnetic moment of the current loop is perpendicular to the Earth's magnetic field, I would use the formula T = m x B, where m is the magnetic moment and B is the magnetic field strength. I would then use the given values to calculate the torque acting on the current loop.

For the second part, I would use the formula for angular acceleration, α = τ/I, where τ is the torque calculated in the first part and I is the rotational inertia about a diameter. I would convert the given rotational inertia from gcm^2 to kgm^2 to ensure consistent units. I would then use the calculated torque and the given rotational inertia to solve for the angular acceleration.

Overall, it is important for a scientist to clarify any uncertainties or questions about the given information, and to use appropriate formulas and units to solve the problem accurately.