Consider a solid, infinitely long, non-conducting cylinder of radius R, carrying
ID: 1876057 • Letter: C
Question
Consider a solid, infinitely long, non-conducting cylinder of radius R, carrying a uniform volume charge density p. In this problem you will derive an expression for the electric field for r<R using Gauss's Law, where r is the perpendicular distance from the z-axis.
1. Draw in a suitable Gaussian cylinder of arbitrary height L on the diagram at right, and write down an expression for the electric fluc throught that cylinder in terms of r, L, and the unknown electric field E. (Remember that r<R)
2. Write down an expression for the total charge contained within the Gaussian cylinder in terms of p, r, and L.
3.Now apply Gauss's Law to the expressions you derived in parts a) and b) and solve for the electric field as a function of r.
Explanation / Answer
form the given diagram
radius of cylinder = R
volume charge density = rho
1. we can draw a gaussean surface which is concentri cylinder with the given cylinder, of radius r < R and length L
2. hecne totak charge inside this gaussean surface is Q
Q = rho*pi*r^2*L
3. now, from gauss law
E*2*pi*r*L = rho*pi*r^2*L/epsilon
E = rho*r/2epsilon