Question

A point dipole of dipole moment -p is located at the center of a grounded (Phi_Shell = 0) spherical conducting shell of radius R. a) Find the electrostatic potential Phi (F) inside the shell.

Answer 1

As the dipole moment p is placed at the center.

We know that, point dipole at origin will have the potential of

(1/4π $\epsilon$ ).(p.cos $\theta$ /r²)

Laplace equation :

A×_lr^l+ B_l/r^l+1

l= 1 is only relevant term ,( held at center)

V(r, $\theta$ )= (A₁r¹+ p/4π $\epsilon$ ₀r²)cos $\theta$ + $\sum$ A_er^l-1p_lcos $\theta$   [ A_e=0]

V(r=R, $\theta$ )= A₁R+ (p/4π $\epsilon$ )(1/R²)=0

V(r, $\theta$ )= p/4π $\epsilon$ ₀(1/r²-r/R³)cos $\theta$