Question

consider the potential v(y,z) =sinky(Ce^kz + De^-kz)

apply the two boundary conditions

a- V(y,z=b)=0

b- V(y=a,z)=0

Answer 1

Equation of the given potential is,

the first boundery condition states,

V(y,z=b)=0 ie V=0 for z=b,

putting z=b in eq 1 we get,

since y is a variable and can have any values hence we cannot take sin ky=0 ,hence,

putting the value of D in eq 1 we will get,

the second boundary condition states,

V(y=a,z)=0 , ie V=0 for y=a;

putting y=a in eq 2 we get,

since z is a variable and can have any values hence we cannot take ,hence,

putting this in eq 2 we will get,

where