Question

What is the magnetic field inside a long solenoid with an iron core, compared to the standard air-core expression?

Options

• \(B = \frac{\mu_0 \mu_r n I}{2}\), because the core halves the field

• \(B = \mu_0 n I\), because the core has no effect on the field

• \(B = \mu_0 \mu_r n I\), because the core amplifies the permeability

• \(B = \frac{\mu_0 n I}{\mu_r}\), because the core reduces the field

Answer 1

With an iron core, the magnetic field inside the solenoid becomes \(B = \mu_0 \mu_r n I\). The iron core amplifies the permeability by the relative permeability factor \(\mu_r\), greatly strengthening the field compared to the air-core case \(B = \mu_0 nI\).