Electricity and magnetism

Electric flux density, divergence and Gauss’s law
1. We have two coaxial cylindrical conductors, the inner or radius and the outer of
radius , each infinite inextent, as shown in Figure 1. Assuming a surface charge
density
in C/m2 on the outer surface of the inner conductor, calculate the electric
field produced by thisinner conductor using Gauss’s law. For symmetry considerations,
assume that the
component is present and that it can be a function only of .
Hint: use as theGaussian surface a cylinder between both conductors of length , and
proceed in a very similar way to that for the infinite line charge.

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Figure 1Two coaxial cylindrical conductors for problem 1
2. Given the electric flux density,

in free space:

a. Find E at point
.
b. Find the total charge within thesphere
.
c. Find the total electric flux leaving the sphere

.

3. In free space, let

.

a. Find the total electric flux passing through the rectangularsurface
, in the direction.
b. Find E at
4. In each of the following parts, find a numerical value for the divergence of D at the
point specified:
a.
b.
c.at
at
at

5. Determine an expression for the volumetric charge density associated with each field D:
a.
b.
c.
6. Given the field
()
()
divergence theoremfor the region bounded by
7. Given the flux density

, evaluate both sides of the
.

, find the total charge within the region
.

8. A cube is defined by. If

.

a. Apply Gauss’s law to find the total flux leaving the closed surface of the cube.
b. Evaluate the divergence of D at the centre of the cube.