Question

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3-2 Two long cylindrical shells of radii r, and r, are arranged coaxially and are charged to the potentials Pa and g, respectively. Find the potential at points between the cylindrical shells.

Answer 1

Now using Laplace & basis on equation nabla^2 phi = 0 Rightarrow 1/r partial differential/partial differential n(r d phi/dr) = 0 on r d phi/dr = C or d phi = C/r dr Rightarrow phi = C ln (r) + d Now using, phi_b = (r = r_b) & phi_a = (r = e_a) Rightarrow phi_b = C ln(r_b) + d----(1) phi_b = C ln (r_a) + d ----(II) thus, phi_b - phi_a = C ln (r_b/r_d) C = (phi_b - phi_a)/ln(r_b/r_a) & d = phi_b - (phi_b - phi_a)/ln(r_b/r_a) ln(r_b) \r\n so phi = C ln (r) + phi = (phi_b - phi_a)/ln (r_b/r_a) ln (r) + phi_b - (phi_b - phi_a)/ln/l_b/r_a) ln phi = (phi_b - phi_a)/ln(r_b/r_a) ln(r) + phi_a ln(r_b) - phi_b ln(r_a)/ln(r_b/r_a) phi = (phi_b - phi_a)/ln(r_b/r_a) { ln (r) + phi ln(r_b) - phi_b ln (r_a)/(phi_b - phi_a}
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