# Video: Physics Past Exam • 2017/2018 • Pack 1 • Question 11A

Physics Past Exam • 2017/2018 • Pack 1 • Question 11A

01:33

### Video Transcript

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 core.

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.