Reference no: EM13957989

Consider a dipole of strength D, oriented along the x-axis and located at the point x = ε/2, y = 0, z = 0, and a dipole of strength -D, oriented along the x-axis at the point x = - ε /2, y = 0, z = 0.  Write the expression for the potential for these two dipoles. Take the limit as ε →0, εD = E = fixed, and show that the limiting potential is given by

u= -E/4π3(3cos2 θ - 1)

This configuration is a quadrupole.  Show that u satisfies

?u = δ"(x) δ(y) δ(z).