Four identical positive point charges sit at (a, a), (−a, a), (−a,−a), and (a,−a) in the z = 0 plane. Very near the origin, the electrostatic potential can be written in the form

(a) Deduce the non-zero terms in this expansion and the algebraic signs of their coefficients. Do not calculate the exact value of the non-zero coefficients.
(b) Sketch electric field lines and equipotentials in the z = 0 plane everywhere inside the square and a little bit outside the square.

Transcribed Image Text:

p(x, y, z) = A + Bx + Cy+ Dz+ Exy + Fxz + Gyz +Hx² + y² + Jz².