# Problem: A large, thin plastic disk with radius R = 1.5 meter carries a uniformly distributed charge of Q = -3x10-5 C. A circular piece of aluminum foil is placed d = 3 mm from the disk, parallel to the disk. The foil has a radius of r = 2 cm and a thickness t = 1 millimeter.A) Show the charge distribution on the close-up foilB) Calculate the magnitude and direction of the electric field at the center of the foil, inside the foil.C) Calculate the magnitude q of the charge on the left circular face of the foil.

###### FREE Expert Solution

From Gauss's law, the electric field is expressed as:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{{\mathbf{q}}_{\mathbf{e}\mathbf{n}\mathbf{c}\mathbf{l}\mathbf{o}\mathbf{s}\mathbf{e}\mathbf{d}}}{\mathbf{4}{\mathbf{\pi \epsilon }}_{\mathbf{0}}{\mathbf{r}}^{\mathbf{2}}}}$

The electric field at point P due to the circular disk is given by:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{\sigma }\mathbf{z}}{\mathbf{2}{\mathbf{\epsilon }}_{\mathbf{0}}}{\mathbf{\left(}}\frac{\mathbf{1}}{\mathbf{z}}{\mathbf{+}}\frac{\mathbf{1}}{\sqrt{{\mathbf{R}}^{\mathbf{2}}\mathbf{+}{\mathbf{z}}^{\mathbf{2}}}}{\mathbf{\right)}}}$, where σ is the charge density, z is the distance from a point to the disk, and R is the radius of the disk.

The electric field due to a conducting surface is:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{\sigma }}{{\mathbf{\epsilon }}_{\mathbf{0}}}}$

The surface charge density, σ is the ratio of the total charge to the surface area.

That is:

$\overline{){\mathbf{\sigma }}{\mathbf{=}}\frac{{\mathbf{Q}}_{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}}{\mathbf{A}}}$

A)

The aluminum foil is 3mm from the plastic disk.

Therefore, the charge will occupy the surface of the aluminum foil due to the charge on the plastic disk.

99% (182 ratings) ###### Problem Details

A large, thin plastic disk with radius R = 1.5 meter carries a uniformly distributed charge of Q = -3x10-5 C. A circular piece of aluminum foil is placed d = 3 mm from the disk, parallel to the disk. The foil has a radius of r = 2 cm and a thickness t = 1 millimeter.

A) Show the charge distribution on the close-up foil

B) Calculate the magnitude and direction of the electric field at the center of the foil, inside the foil.

C) Calculate the magnitude q of the charge on the left circular face of the foil.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Gauss' Law concept. You can view video lessons to learn Gauss' Law. Or if you need more Gauss' Law practice, you can also practice Gauss' Law practice problems.