Problem set 09

Problem 1

(a) Establish the relation between the two boundary conditions

$$\hat{\mathbf{a}}_{n2}\cdot\left(\mathbf{D}_1 -\mathbf{D}_2\right) = \sigma \quad \mathrm{and} \quad \hat{\mathbf{a}}_{n2}\times\left(\mathbf{H}_1 -\mathbf{H}_2\right) = \mathbf{J}_s.$$

(b) Find the relation between the two boundary conditions

$$\hat{\mathbf{a}}_{n2}\cdot\left(\mathbf{B}_1 -\mathbf{B}_2\right) = 0 \quad \mathrm{and} \quad \hat{\mathbf{a}}_{n2}\times\left(\mathbf{E}_1 -\mathbf{E}_2\right) = 0,$$

which are usually written as

$$E_{1t} = E_{2t} \quad \mathrm{and} \quad B_{1n} = B_{2n}.$$

The problem is due Monday March 17 2025 at 20:00