Question

2. A slab of nonconductive material is perpendicular to the
*z*-axis, centered on the origin, has a total thickness of
40 mm, and isinfinite along the other two axes. It has a uniform
volumetric charge density of -108 pC/m^3. It contains a perfectly
spherical bubble with no charge or material in it. The bubble is
also centered on the origin and has a radius of 10 mm. Find
expressions for the electric field vector at all points on the
positive *z*-axis. Use 9x10^-12 C^2/N·m^2 for the
permittivity in all regions.

please show steps, thank you!

Answer #1

for z > 20 mm

using equation E = / 2_{o}

E = - 108 X 10^{-12} X 0.04 / ( 2 X 9 X10^{-12}
) + ( 1 / 4 X 3.14 X 9 X 10^{-12}) X 108 X 10^{-12}
X (4/3 X 3.14 X 0.01) / z

**E = ( - 0.24 + 4 X 10 ^{-6} / z )
N/C**

for z < 10 mm

E = - 0.24 z / 0.02 + z / 3_{o}

= - 12 z + 108 X 10^{-12} z / 3 X 9 X
10^{-12}

**= - 8 z N/C**

for 10<z<20mm

**= - 12 z + 4 X 10 ^{-6} /z**

**here z value in meters.**

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