Answer to Question #91084 in Electricity and Magnetism for Vigil

Question

Is a electromagnet more powerful if the centre core is long than short is longer the better just like adding more wraps

Answer 1

The answer is no.

In our everyday life a powerful magnet is the one that can attract and lift up a heavy piece of steel or is the one which you cant separate from the freezer door. In this case the magnetic force depends on the cross-sectional area of the core rather than on its length. Electromagnets use only one of their ends. If you google for industrial electromagnets, you'll notice that they all are not thick or long but wide, because the magnetic flux that produces the attractive force is defined by the current in the magnet, number if turns and its area $A$. It is much easier to increase the area than the field (or current $I$). The force of an electromagnet is inversely proportional to its length $l$:

$$F=\frac{CANI}{l}.$$

So, longer electromagnets on the whole are not better than short and wide ones. Longer are just more expensive.

The same answer if you mean the real power or energy. The energy of the electromagnet:

$$E=\frac{1}{2}LI^2,$$

where inductance $L$ is inversely proportional to its length and directly proportional to the number of turns and its area:

$$L=\frac{k\mu_0N^2A}{l}.$$

Also, pay your attention to the coefficient $k$, which represents relative permittivity of the material inside the magnet. For steel this quantity is much higher than unity, so with steel core (not long) inside the electromagnet it can store more energy and it can be considered as more powerful.