Electromagnets and Factors Affecting Their Strength

What an electromagnet is. An electromagnet is a magnet whose field is produced not by permanently aligned atomic dipoles (as in a bar magnet) but by an electric current flowing through a coil, usually a solenoid wound around a core of magnetic material -- and, unlike a permanent magnet, it can be switched on and off, and its strength adjusted, simply by controlling the current. The field at the centre of a long solenoid of $n$ turns per unit length carrying current $I$, with a core of relative permeability $\mu_r$ filling it, is

(reducing to the plain air-core solenoid formula $B=\mu_0nI$ when $\mu_r=1$) -- and this single expression identifies every factor that decides an electromagnet's strength.

1. Number of turns per unit length, $n$. Since $B\propto n$, winding the coil with more turns packed into the same length directly increases the field for a given current -- each additional turn contributes its own current loop's worth of field (Section 1.2), and these add.

2. Current, $I$. Since $B\propto I$, increasing the current through the coil directly increases the field, up to the practical limits set by the wire's resistive (Joule) heating and the core's own saturation (Section 1.10) -- beyond saturation, a further increase in $H$ (and hence in $I$) produces almost no further increase in $B$.

3. The core material -- why soft iron, not steel. Replacing an air core ($\mu_r\approx1$) with a soft-iron core ($\mu_r$ typically in the hundreds to low thousands) multiplies the field by that same large factor for identical winding and current (Numerical 9 works this out directly) -- by far the single biggest lever on an electromagnet's strength. Soft iron, specifically, is chosen over a magnetically HARD material such as steel because of its LOW retentivity and LOW coercivity (Section 1.11): it magnetises to a strong field almost instantly when the current is switched on, and -- just as importantly -- demagnetises again almost completely the instant the current is switched off, so the device behaves as a true on/off magnet rather than remaining permanently (and unpredictably) magnetised. A hard material like steel would retain much of its magnetism even with the current off, defeating the entire purpose of an electromagnet. …