Download 1. The electric field intensity inside a dielectric sphere of radius a

1. The electric field intensity inside a dielectric sphere of radius a, centered at the origin is given
by
E = ρor aR
If the permittivity of the dielectric is ε, calculate the total charge inside the sphere.
2. A sphere of radius R has a spherically symmetric charge density ρ(r)=ρo(1-r/R) where r is the
distance from the center. Calculate the energy stored in the whole space as well as the energy
stored within the volume of the sphere.
3. Two point charges are located above a grounded conducting plane as shown in the Figure
below. Calculate the electric field intensity in the space above the plane. Also find the induced
surface charge.
4. A point charge Q [C] is surrounded by a hollow conducting sphere as shown in the figure below
Calculate:
(a) The electric field intensity and electric potential everywhere in space. Plot the electric field
intensity and the potential.
(b) The surface charge densities on the inner and outer surfaces of the conducting shell.
5. The surface 2x + y + z = 4 separates two regions. The relative permittivity of the region
containing the origin is εr1 = 2 and the relative permittivity of the region on the other side of the
plane is εr2 = 3. The electric field intensity in region I near the interface is: E1 = ax + 2ay + 2az.
There is a surface charge density ρs = ε0√6 C/m2 at the interface between the two regions.
Determine the electric field intensity and the electric flux density in the second region near the
interface.
6. For a coaxial cable of inner conductor radius a and outer conductor radius b and a dielectric r
in-between, assume a charge density v  o  is added in the dielectric region. Use Poisson’s
equation to derive an expression for V and E. Calculate s on each plate. The potential at the inner
surface is V0 and the outer surface is grounded.
7. Given D = 2a + sin  az C/m2, find the electric flux passing through the surface defined by
2.0 ≤ ≤ m, 90. ≤ ≤ 180, and 0≤ z ≤ 4.0 m. Also verify the divergence theorem in this
region.
8. An inhomogeneous dielectric fills a parallel plate capacitor of surface area A and thickness d.
You are given r = 3(1 + z), where z is measured from the bottom plate. Determine the capacitance.
9. A conical section of material extends from 2.0 cm ≤ r ≤ 9.0 cm for 0 ≤  ≤ 30 with r = 9.0 .
Conductive plates are placed at each radial end of the section. Determine the capacitance of the
section.
10.