Physics/Calculating the field strength of an electromagnet
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I am interested in the behavior of electromagnets, and I would like to ask a question about the influence of the size and shape of the soft iron core in a solenoid.
Calculating the strength of an electromagnet based on the presence or absence of the iron core is something that seems reasonably straightforward to me, but I am wondering how the field strength calculations might be affected in the following situation.
Imagine you have a copper coil that is fixed in position by some kind of housing. Inside the coil is an iron rod, but the rod is thinner than the coil, for example, the radius of the coil is two centimeters and the rod's is 1.8 centimeters. The rod is loose inside the coil, and can move from side to side and up and down. What would happen in this situation? Would the rod be moved up or down by the magnetic field created by the coil, or would it be moved sideways and stick to the coil?
How would you go about calculating the magnetic field strength of such an electromagnet? I am assuming that the air gap between the coil and the rod would reduce the magnetic field strength, is that correct?
Your insight would be much appreciated. Thanks very much.
Please forgive my delay in responding -- it's the only way I can think of, to ensure that I do not assist with academic or professional efforts, of which homework is just one type.
In the situation you describe above (I'm not sure why you specified 1.8 cm and 2.0 cm, as that is almost irrelevant to the question), current through the copper wire would create a magnetic field within the core of the wound coil. The iron within this core would strengthen that field. Any force on the iron rod would be too small to cause significant motion.
The size of the B-field within the coil (ignoring edge effects) can be found by this formula:
Note that the size of the B-field SOLELY FROM THE CURRENT IN THE COIL depends on the current (no surprise) and the number of turns per unit length, but not on the radius from the center. The increase in the B-field within the iron core depends on the magnetic properties of the iron. However, in the air gap between the iron rod and the copper coil, the B-field would be no stronger than it would be if there were no iron rod within the copper coil (again, ignoring edge effects). In that sense, the air gap does not reduce the magnetic field strength, it simply fails to increase it.