The functions V 1 (, , z) and V 2 (, , z) both satisfy Laplaces equation
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The functions V1(ρ, ϕ, z) and V2(ρ, ϕ, z) both satisfy Laplace’s equation in the region a < ρ < b, 0 ≤ v < 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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