The functions V1(ρ,ϕ, z) and V2(ρ, ϕ, z) both satisfy Laplace’s equation in the region a<ρ<b, 0 ≤ ϕ<2π, - L<z<L; each is zero on the surfaces ρ = b for - L<z<L; z = -L for a<ρ<b; and z = L for a<ρ<b; and each is 100 V on the surface ρ = a for - L<z<L. (a) In the region specified, is Laplace’s equation satisfied by the functions V1 + V2, V1 - V2, V1 + 3, and V1V2? (b) On the boundary surfaces specified, are the potential values given in this problem obtained from the functions V1 + V2, V1 - V2, V1 + 3, and V1V2? (c) Are the functions V1 + V2, V1 - V2, V1 + 3, and V1V2 identical with V1?
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