# Attraction between two solenoids

I have been asked to calculate the attraction between two solenoids that are positioned in 'series' N-S N-S and have a space 'x' between them.

I tried to approximate the attraction between them by using the equation for attraction between cylinderical bar magnets:

F=\left[\frac {B_0^2 A^2 \left( L^2+R^2 \right)} {\pi\mu_0L^2}\right] \left[{\frac 1 {x^2}} + {\frac 1 {(x+2L)^2}} - {\frac 2 {(x+L)^2}} \right]

where

B0 is the magnetic flux density very close to each pole, in T,
A is the area of each pole, in m2,
L is the length of each magnet, in m,
R is the radius of each magnet, in m, and
x is the separation between the two magnets, in m

(its from http://en.wikipedia.org/wiki/Force_between_magnets)

I have been told this is not an appropriate equation. Can anyone help me understand why, and what I should do instead?

LB

Forgot to mention, I know the size of solenoids and the flowing current so I could calculate the magnetic field size to use in the bar magnet equation.

rude man
Homework Helper
Gold Member
My stab at it:

Each solenoid has N turns. Using the formula for the force between two parallel wires carrying currents iA and iB, take the loop of solenoid A closest to solenoid B and determine the force between it and the closest loop of solenoid B. Then take the closest loop of A and get the force between it and the second-closest loop of B, etc. Then repeat for all the loops of A.

You don't want a discrete formula so assume a winding density of n turns/unit length and do a continuous integration.

Hopefully you'll get other suggestions. Not sure this is the best way to proceed.

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