Calculating the centre of mass of a U shaped conductor/Magnetic Field

[Mathoholic!]

Homework Statement

The exercise asks you to calculate the magnitude of the magnetic field (\vec{B}=B\hat{z}), knowing that the U shaped conductor is initially parallel to Oyz plane and then rotated around the y-axis to a stable position defined by θ (angle) with the vertical axis (z).

The U shaped conductor has a linear density of mass, ρ (g/cm), with a horizontal length d, and a vertical length L. There is also a flow of electric charge (I) traveling the conductor.

Homework Equations

The Attempt at a Solution

To calculate the magnitude of the magnetic field I used the definition of torque (τ), equating the torque of gravity to the torque of the magnetic force so that the conductor is in equilibrium (θ). But to calculate the torque I have to know how to calculate its centre of mass, with which I'm having a hard time...

I'd appreciate some feedback on how to proceed in this exercise. :)

 

[TSny]

If I'm understanding the set up, the U-shape conductor is made of three conducting rods. To find the center of mass: replace each rod by a point particle located at the center of the rod with mass equal to the mass of the rod. Then you just have to find the CM of the three particles.

 

[Mathoholic!]

If I'm understanding the set up, the U-shape conductor is made of three conducting rods. To find the center of mass: replace each rod by a point particle located at the center of the rod with mass equal to the mass of the rod. Then you just have to find the CM of the three particles.

Thanks, I've got it know :)