Chapter 2.5, Problem 2.54P

(a)

To determine

The electric field for the given field in the form of charge distribution $\rho$ .

(b)

To determine

To Explain:Whether, the electric field consists of a scalar potential.

(c)

To determine

The electric potential for a point charge $q$ .

(d)

To determine

To Prove

${\displaystyle \underset{S}{\oint }E.da}+\frac{1}{{\lambda }^2}{\displaystyle \underset{V}{\int }Vd\tau }=\frac{q}{{\epsilon }_o}$

(e)

To determine

To Prove:

${\displaystyle \underset{S}{\oint }E.da}+\frac{1}{{\lambda }^2}{\displaystyle \underset{V}{\int }Vd\tau }=\frac{1}{{\epsilon }_o}{Q}_{enc}$

(f)

To determine

To Draw:A triangle diagram using differential form of Gauss law in terms of charge distribution $\rho$ and Poisson’s equation.

(g)

To determine

To Show:

Some of charge is uniformly distributed inside the conductor itself.