3. Cylindrical Symmetry Calculate the electric eld for each of the following con

ID: 1423819 • Letter: 3

Question

3. Cylindrical Symmetry

Calculate the electric eld for each of the following congurations. In each case, draw a clear picture

indicating your Gaussian surface and evaluate all integrals explicitly.

a) Consider a long (innite), thin insulating rod carrying uniform linear charge density . What is

the electric eld a distance d away from the rod?

b) Replace the thin rod in part (a) with a cylinder of radius R. The charge density is still uniform,

but now volumetric . Calculate the electric eld for points inside the cylinder.

c) Using the same charge distribution in (b), calculate the eld outside the cylinder.

d) Check to see if your answers to (b) and (c) give a consistent result at the boundary of the cylinder.

Sketch a graph of the electric eld strength as a function of radial distance.

a) E * (2pidL) = L/ 0

=> E = / (2*pi*d*0)

b) E * ( 2pidL) = *pi*d2*L/0

=> E = *d / 20

c) E * ( 2pidL) = *pi*R2*L/0

=> E = *R2 / 2d0

d) At Surface Put value of d = R in (b) and (c) parts

=> E = *R / 20

=> consistent result at the boundary of the cylinder.

e) For inside of cylinder

=> E * 2*pi *r *L = 2*pi*L* o*r2/(20)

=> E = o*r/(20R)

For outside cylinder

=> E * 2*pi *r *L = pi*L* o*r/(20)

=> E = o/(20)

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