Compare the self-induction
coefficient of a solenoid under the following conditions, stating whether there is
more or less self-induction in each case. The solenoid has an iron core. The solenoid does not have an iron
We can start by considering a
solenoid that has a length 𝑙, a cross-sectional area 𝐴, and 𝑁 turns in its
coil. The self-induction coefficient 𝐿
is equal to 𝑁 squared times 𝐴 divided by the length all multiplied by the
permeability of the core of the solenoid. That core material might simply be
air as we drawn it here or it could be a solid material designed to increase the
magnetic susceptibility of the solenoid.
In general, the permeability 𝜇 is
equal to the relative permeability of the material making of the solenoid core
multiplied by the permeability of free space 𝜇 nought. As we consider in this exercise a
solenoid that has an iron core versus one that does not, the effect of putting an
iron core inside our solenoid would be to raise the permeability of this core
material. And we see by the relationship for
the self-induction coefficient that raising 𝜇 increases 𝐿.
For the solenoid that does have an
iron core, we can say that the self-induction coefficient is greater than if there
is no iron core. And for the solenoid that does not
have an iron core, we can say that the self-induction coefficient is less than if
there is an iron core. This is the comparison of the
self-induction coefficient of a solenoid with and without an iron core.