# Problem: A thin, horizontal, 20-cm-diameter copper plate is charged to 4.0 nC . Assume that the electrons are uniformly distributed on the surfacea) What is the strength of the electric field 0.1 mm above the center of the top surface of the plate?b) What is the direction of the electric field 0.1 mm above the center of the top surface of the plate? (Away or toward)c) What is the strength of the electric field at the plate's center of mass?d) What is the strength of the electric field 0.1 mm below the center of the bottom surface of the plate?e) What is the direction of the electric field 0.1 mm below the center of the bottom surface of the plate? (Away or toward plate)

###### FREE Expert Solution

The electric field of a uniformly charged surface:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{\sigma }}{\mathbf{2}{\mathbf{\epsilon }}_{\mathbf{0}}}{\mathbf{\left(}}{\mathbf{1}}{\mathbf{-}}\frac{\mathbf{x}}{\sqrt{{\mathbit{r}}^{\mathbf{2}}\mathbf{+}{\mathbf{x}}^{\mathbf{2}}}}{\mathbf{\right)}}}$, x is the distance above the center of the surface of the plate.

Diameter, d = 20 cm

Radius, r = d/2 = 20/2 = 10 cm = 0.1 m

x = 0.1 mm = 0.1 × 10-3 m

The surface charge density, σ

$\overline{){\mathbf{\sigma }}{\mathbf{=}}\frac{\mathbf{q}}{\mathbf{A}}}$

94% (473 ratings) ###### Problem Details

A thin, horizontal, 20-cm-diameter copper plate is charged to 4.0 nC . Assume that the electrons are uniformly distributed on the surface

a) What is the strength of the electric field 0.1 mm above the center of the top surface of the plate?

b) What is the direction of the electric field 0.1 mm above the center of the top surface of the plate? (Away or toward)

c) What is the strength of the electric field at the plate's center of mass?

d) What is the strength of the electric field 0.1 mm below the center of the bottom surface of the plate?

e) What is the direction of the electric field 0.1 mm below the center of the bottom surface of the plate? (Away or toward plate)

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