# 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*r*_{a}= 1 mm and*V*= 100*V*at*r*_{b}= 20 mm. Neglect fringing.Solution

Since

*V*varies with*r*only, Laplaceâ€™s equation can be written as,Integrating twice,

where,
Applying boundary conditions, we get,
Solving,
Hence, the field intensity is given as,

*A*and*B*are constants.At

*r*=*r*_{a}= 0.001,*V*= 0 â‡’ 0 =*A*ln(0.001) +*B*At

*r*=*r*_{b}= 0.02,*V*= 100 â‡’ 100 =*A*ln(0.02) +*B**A*= 33.36 and*B*= 230.49