For a perfectly conducting and perfectly dielectric interface, I understood that tangential component of electric field is zero and continuous. But I have read that the normal component of magnetic field is also zero. I have read this in the chapter of guided waves between a pair of infinite parallel conducting planes. While I understand that variation in normal component of magnetic field at the interface would produce a non-zero tangential electric field which violates the first condition, why can't there be a constant normal component of magnetic field at the boundary of the conducting plane? Why should it be zero?
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1 Answer
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There can be, so long as in addition to being constant, it is curl-free.
Ampere's law says that the curl of magnetic field is produced by a current density or time-varying electric field. Since neither is present just outside the interface, then the magnetic field is curl-free there.
Faraday's law says that a time-varying normal component of the magnetic field would produce a non-zero tangential electric field, so the normal component of the magnetic must be stationary. In fact, whatever the curl of the electric field, you can always add a stationary magnetic field without changing the RHS of Faraday's law.
The above conditions allow a stationary, curl-free (and of course divergence-free) magnetic field to be present. The normal component of that field will be continuous across the boundary.
A stationary, curl-free, magnetic field can be superposed onto any solution of Maxwell's equations without affecting the time-dependent electric and magnetic fields.
