Gauss' Law for Magnetic Fields — Question 6

Question 6

Normal magnetic field is continuous across a material interface

A thin pillbox straddles an interface. The magnetic field remains finite on both sides. Field 1 has magnitude .600 T and angle 60 degrees to the interface normal; field 2 makes 30 degrees to the same normal and has the same normal sign.

1. Derive continuity of the normal field from shrinking pillbox flux.

2. Find the magnitude of field 2.

Question 6 - Solution

Normal magnetic field is continuous across a material interface

(a) Method and calculation

$$\Phi=(B_{2n}-B_{1n})A+O(h)=0,\quad h\to0.$$$$\boxed{B_{2n}=B_{1n}}.$$

(b) Interpretation and further calculation

$$B_2\cos30^\circ=B_1\cos60^\circ.$$$$\boxed{B_2=.600\frac{1/2}{\sqrt3/2}=.346410\,T}.$$

Physical check

Material response can change field direction and magnitude while preserving its normal component.