## Electronics

#### Magnetic Dipole Moment

• BLHesterman
Subscriber

Could someone explain how to calculate the magnetic dipole moment using the Maxwell Calculator?

• Paul Larsen
Ansys Employee

There are are a few definitions/calculations of magnetic moments.  The easiest is defined with respect to torque aligning to an external field.  So, the easiest way to calculate the dipole moment is to apply an external field (or use a Helmholtz coil to create a uniform field around the object), and then calculate the torque vs angle around the center of the object/assembly.  So, first you might try to create a uniform field without any objects, for which you could use a Helmholtz coil arrangement.  Or you could use a combination of boundary conditions (Tangential H-field to define the direction tangent, and Zero Tangent to define the ends where the flux enters/exits the domain).  Then insert the geometry, and use a Torque parameter on the entire assembly to calculate the T = m x B moment torque.

• BLHesterman
Subscriber

Thanks for the information.  One issue of this approach is determining the center point of a complicated set of conductors.

I found this information on Wikipedia: https://en.wikipedia.org/wiki/Magnetic_moment#Localized_current_distributions

I have been trying to implement this in the fields calculator.  I can define r in terms of x, y & z, and enter r x j.  I'm not sure how to implement the integral. My intention is to integrate over the current-carrying conductors in a magnetostatic simulation.

• Paul Larsen
Ansys Employee

Hi Bryce,  All methods that I am aware of require either assumptions, estimates, or maybe iterative methods of determining the center reference point (such as your r-position reference).

You can perform the calculation around one axis at a time, so you could calculate m_z for positions with reference to the global Z-axis with the following Field Calculator commands:

• Function > Scalar: X (global X position)

• Vec? > VecX

• Function > Scalar: Y (global Y position)

• Vec? > VecY

• + (this is a radial position vector, you can add VecZ position to obtain full position)

• Quantity > CurrentDensity (J)

• Cross

• Scal? > ScalarZ (integral needs to be performed on scalar components separately)

• Geometry > Volume Object

• Integral

You can then repeat for X and Z axis.  Apply the 1/2 scaling at any time.