Discussion
Which component of the electric field intensity is always continuous at the boundary ?
Answer: A
The tangential component of the electric field is always continuous at a boundary.
Applying \(\oint \mathbf{E} \cdot d\mathbf{l} = 0\) to a thin rectangular loop straddling the interface gives \(E_{t1} = E_{t2}\), whatever the two media are. The normal component behaves differently: Gauss's law gives \(D_{n1} - D_{n2} = \rho_{s}\), so the normal component of \(\mathbf{E}\) jumps whenever the permittivities differ or a surface charge is present.
'Horizontal' and 'vertical' are not defined relative to the boundary, so they are not the components boundary conditions are written in, and the normal component is continuous only in special cases.
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