# Solved Problem-2

Problem-2
Find the potential and electric field intensity for the region between two concentric right circular cylinders, where V = 0 at ra = 1 mm and V = 100 V at rb = 20 mm. Neglect fringing.
Solution
Since V varies with r only, Laplaceâ€™s equation can be written as,

Integrating twice,

where, A and B are constants.

Applying boundary conditions, we get,

At r = ra = 0.001, V = 0 â‡’ 0 = A ln(0.001) + B

At r = rb = 0.02, V = 100 â‡’ 100 = A ln(0.02) + B

Solving, A = 33.36 and B = 230.49

Hence, the field intensity is given as,