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## Homework Statement

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

rv′′+2v′=0, r1≤r≤r2

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.

## Homework Equations

rv′′+2v′=0

## The Attempt at a Solution

I tried to use v(r)=r

^{m}as a solution:

v'(r)=mr

^{m}

v''(r)=m

^{2}r

^{m}

and sub back in:

m

^{2}r

^{m+1}+2mr

^{m}=0

this yields:

m(mr+2)=0, which leads me no where near the solution

Please help