Chapter 6, Problem 6.33P

The functions V₁ (p, ∅, z) and V₂(p, ∅, z) both satisfy Laplace' s equation in the region a < p < b,0 < ∅ < -z,L < z < L; each is zero on the surfaces p = b for—L < Z, z = -L and a < p < b and z=L for a < p < b: and each is 100 V on the surface p=a for - L < z < L. (a) In the region specified; is L aplace' & equation sati s field by the functions V₁\ - V₂>, V\ - f ⁷: ₌ V\ + 3 _r and V\ V2 ? (b) On the boundary surface s specified; are the potential values given in this problem obtained from the functions V\ + V₂: V₃, - Vi._ V\ + 3. and V\ V₂ ? (c) Are the functions V_ - Vi: Y\ — V₂, V\ - 3, and V\ Vj identical with V?