Question

Consider a long cylindrical charge distribution of radius R with a uniform charge density rho. (a) Find the electric field at distance r from the axis where r R.

Answer 1

Answer:

E=Ur/2E_{0}

Explanation:

Consider a long cylindrical charge distribution of radius R with a uniform charge density rho. (a) Find the electric field at distance r from the axis where r R.

to find the electric point inside the cylinder

r=radius of the cylinder

A=curved surface area of the cylinder

∪=charge density

Q=is the net charge

V=volume of the cylinder

Q=UV

volume of the gaussian cylinder =$\pi r^{2} l$

Q=$\pi r^{2} l$U

area A=$2\pi rl$

Write the expression   Gaussian law

∅=∫EdA=Q/$E_{0}$..........................1

E_{0} is the permittivity of free space and Eois the electric field

rewriting the equation 1 , we have

EA=Q/E_{0}

substituting for A and also for Volume V in the equation above

E*$2\pi rl$=$\pi r^{2} l$U/E_{0}

E=Ur/2E_{0}