The electric potential energy v(r) of a charged particle located between two uniformly charged concentric spheres with radii r1 and r2 satisfies the second order differential equation
where r is the distance of the charged particle from the common centre of the spheres.
(a) Determine the general solution of the differential equation, by trying a solution of the form v(r)=rm, m∈R.
(b) Using your answer to part (a), find the electric potential energy of a charged particle between two concentric spheres with radii r1 = 2 cm and r2 = 20 cm, kept at potentials v1 = 220 Volts and v2 = 130 Volts respectively.
The Attempt at a Solution
I tried to use v(r)=rm as a solution:
and sub back in:
m(mr+2)=0, which leads me no where near the solution