Physics

Physics

Problem

A long solenoid of turn density nn carries a steady current II. If an iron core of relative permeability μr\mu_r is inserted completely so that it fills the interior, the magnetic field inside the solenoid becomes a) 1μr\dfrac{1}{\mu_r} times its initial value b) μr\mu_r times its initial value c) μr\sqrt{\mu_r} times its initial value d) unchanged
Intuitive explanation

The key insight is that inserting a magnetic material doesn't change the current or coil geometry—it amplifies the field by a factor equal to the material's relative permeability μr\mu_r. Start with the field formula for an empty solenoid, B0=μ0nIB_0 = \mu_0 n I, then recognize that an iron core multiplies this by μr\mu_r because the material's atomic dipoles align and reinforce the applied field. The new field is simply the old field scaled up by the material's magnetic response.

Intuitive explanation

The key insight is that inserting a magnetic material doesn't change the current or coil geometry—it amplifies the field by a factor equal to the material's relative permeability μr\mu_r. Start with the field formula for an empty solenoid, B0=μ0nIB_0 = \mu_0 n I, then recognize that an iron core multiplies this by μr\mu_r because the material's atomic dipoles align and reinforce the applied field. The new field is simply the old field scaled up by the material's magnetic response.

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