Magnetic Materials — Question 5

Question 5

Magnetic refraction follows two different interface continuity laws

Two linear isotropic media meet at a plane with no free surface current. Their permeabilities are mu1 and mu2. Field directions make angles theta1 and theta2 with the interface normal.

1. Use normal B and tangential H continuity to derive the relation between the angles.

2. For mu2=3mu1 and theta1=30 degrees, find theta2 and B2/B1.

Question 5 - Solution

Magnetic refraction follows two different interface continuity laws

(a) Method and calculation

$$B_1\cos\theta_1=B_2\cos\theta_2,\quad \frac{B_1\sin\theta_1}{\mu_1}=\frac{B_2\sin\theta_2}{\mu_2}.$$$$\boxed{\tan\theta_2=(\mu_2/\mu_1)\tan\theta_1}.$$

(b) Interpretation and further calculation

$$\tan\theta_2=\sqrt3\Rightarrow\boxed{\theta_2=60^\circ}.$$$$\boxed{B_2/B_1=\cos30^\circ/\cos60^\circ=\sqrt3}.$$

Physical check

Angles are measured from the normal; using angles from the surface would invert the tangent relation.