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.