# Homework Help: Force On Rod Inserted In Solenoid

1. Feb 17, 2010

### zzachattack2

1. The problem statement, all variables and given/known data

A long cylindrical rod (permeability u , length L0, radius R) is partially inserted into a long
solenoid (length L1, radius R, turn density n, and fixed current I)

How large is the force on the rod? Our hint is to first calculate the total energy in the field.

2. Relevant equations

W= 1/2*L*I^2 for calculating energy and finding force from energy, F = dW/dL

3. The attempt at a solution

So my attempt to solve this was of course first find the energy stored in the field. Of course the Inductance of the solenoid is just L=u0*n^2*pi*R^2*L1 and this can just be plugged into the formula above for finding total energy in the field. My guess is that you should find how the total magnetic field changes by inserting a permeable core, and thus how the energy in the field changes. This difference can be used to calculate the force on the rod. However I'm having alot of trouble finding the difference in energy when the rod is "partially" inserted. Any ideas? Thanks.