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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:

E=qenclosed4πε0r2

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

E=σz2ε0(1z+1R2+z2), 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:

E=σε0

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

That is:

σ=QtotalA

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.

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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.

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