A pair of perfectly conducting electrodes traps a magnetic field, as shown in Fig. 6P.7. One electrode is planar and at y = 0, the other has a small sinusoidal variation given as a

function of space and time. Both boundaries can be considered perfect conductors, so that n - B = 0 on their surfaces. In what follows, assume that a
where A is the flux trapped between the plates (per unit length in the z-direction) and h, and h, are small compared with A/µod

(a) Find the perturbation components h. and h,.

(b) The solutions in part (a) must satisfy the boundary conditions: n X E = (n. v)B [boundary condition (6.2.22) of Table 6.1]. Compute the electric field intensity by using the magnetic field found in part (a). Now check to see that this boundary condition is satisfied to linear terms.