1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Anti-Helmholtz coil configuration

  1. Jun 20, 2012 #1

    Say I have to coils in the anti-Helmholtz configuration as in the attached picture. It is pretty easy to find the field along the z-direction, as this is introduced in introductory EM. However say that I would like to know the field along the x-direction. This I don't know how to find.

    What I *do* know is that the Maxwell Equations (div B = 0) tell me that
    \frac{dB}{dx} = \frac{dB}{dy} = -\frac{1}{2}\frac{dB}{dz}
    But does this imply that the field along x, B(x), is simply -B(z), the negated B-field along the z-direction?


    Attached Files:

  2. jcsd
  3. Jun 21, 2012 #2


    User Avatar
    2017 Award

    Staff: Mentor

    div B = 0 is equal to [itex]\frac{\partial B_x}{\partial x} + \frac{\partial B_y}{\partial y} = - \frac{\partial B_z}{\partial z}[/itex]
    Using symmetry, x and y must be the same, therefore [itex]\frac{\partial B_x}{\partial x}= - \frac{1}{2}\frac{\partial B_z}{\partial z}[/itex]
    This does not give you any magnetic field! It is just the derivative of the field at some specific point - probably along the central axis. Looking at the (x,y)-plane right in the middle of the coils, you have a field going radially inwards/outwards (depending on the orientation).
  4. Jun 23, 2012 #3
    Thanks, that was kind of you.
  5. Jun 23, 2012 #4


    User Avatar
    Science Advisor
    Gold Member

    The off-axis field from a current loop is written as an expansion in elliptic integrals (or sometimes other functions, depending on the coordinate system you choose). Here is a site that came up in a Google search for off-axis field from a loop:
    but there are many others. The field from a pair of coils is then a sum of the fields from the individual loops.

    More extensive derivations/explanations are found in advanced E&M texts like those by Jackson, Smythe, and Stratton.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook