where l is distance and v is the volume of the material. It needs emphasizing that this formula will give significant overestimates for ferromagnetic materials. For them the internal 'demagnetizing field' leads to lower values of force than equation FRL would suggest. Demagnetizing fields only have exact analytical solutions for spheroidally shaped specimens. Consult a text such as Jiles for details on correcting for demagnetizing fields.
A simple experiment with a solenoid
A 'solenoid' is the term used to describe the type of electromagnet supplied with an iron piston or plunger pulled in by the field generated by current in a coil. Experimental arrangement to measure solenoid pull. Solenoids are frequently used to operate valves, release locks or operate ratchets and so on. Equation EFS above suggests that the pull of a solenoid should be related to the square of the coil current. Take a medium sized 12 volt solenoid (having a plunger about 13 mm diameter) and test this out by attaching it to a spring balance as shown in the figure here. Measurements are made as follows
1.Set a high coil current by turning the power supply up towards 12 volts.
2.Push the plunger in until it is retained by the field.
3.Reduce the length of the cord until either the balance reads maximum load or the solenoid just retains the plunger. A turnbuckle is handy here.
4.Make a note of the force measured by the balance.
5.Reduce the current slowly, keeping an eye on the meter reading, until the solenoid lets go, and note the current. The restraining cord is essential unless you want to be hit in the eye by a lump of iron moving at very high speed :-)
Repeat the sequence, slackening the cord on the balance each time to obtain a lower force. This gave the line, shown below, which has a slope of about 1.1.