Two point charges q and q are located on the z axis at z a and z a, respectively (a) Find the electrostatic potential as an expansion in spherical harmonics and powers of r for both r a and r a (b) Keeping the product qa p 2 constant, take the limit of a 0 and find the potential for 0 This is by definition a dipole along the z axis and its potential (c) Suppose now that the dipole of part b is surrounded by a grounded spherical shell of radius b concentric with the origin By linear superposition find the potential everywhere inside the shell

Question: Two point charges q and q are located on the z axis at z = + a and z = a, respectively. (a) Find the

Two point charges q and –q are located on the z axis at z = + a and z = –a, respectively.

(a) Find the electrostatic potential as an expansion in spherical harmonics and powers of r for both r > a and r < a.

(b) Keeping the product qa = p/2 constant, take the limit of a → 0 and find the potential for г ≠ 0. This is by definition a dipole along the z axis and its potential.

(c) Suppose now that the dipole of part b is surrounded by a grounded spherical shell of radius b concentric with the origin. By linear superposition find the potential everywhere inside the shell

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