[Numerical Analysis]

It is Numerical Analysis. Please use Matlab language. !!

The electric field is related to the charge density by the divergence relationship where E is electric field, ? charge density, and to is permittivity. The electric field is related to the electric potential by a gradient relationship Therefore the potential is related to the charge density by Poisson's equation ED In a charge-free region of space, this becomes Laplace's equation, The walls of a rectangular cylinder are constrained in potential as shown in 2. The walls at r 0, a and y 0 have zero potential, while those at yb have the potential distributions V, respectively The region inside the cylinder is free space. v(t) y b Figure 2: Setup of the rectangular cylinder Assume that a b1 and V-1. Determine the potential in the free region inside the cylinder . Plot the potential ?(z, y) and error, |?(r3)-0,(z, y)|, where the exact potential distribution is RT o 4V sinh_yT n=1,odd sinh- and 0