A charged paint is spread in a very thin uniform layer over the surface of a pla

Question

A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 12.0 cm , giving it a charge of -59.0 C . Find the electric field just outside the paint layer. Express your answer with the appropriate units. Enter positive value if the field is directed radially inward and negative value if the field is directed radially outward? Find the electric field 7.00 cm outside the surface of the paint layer. Express your answer with the appropriate units. Enter positive value if the field is directed radially inward and negative value if the field is directed radially outward?

Explanation / Answer

If the charge is uniformly distributed on the surface of a sphere, the electric field outside the sphere will be the same as if the entire charge were concentrated in the center of the sphere. The electric field inside the sphere would be zero.

Because the electric field in a would be measured inside the (uniformly-charged) sphere, the electric field for part a would be zero. For the other two cases, we get
E = q / (4or²)

r = 0.120 m, so the electric field would be
-5.90e-8 C / (4(8.85e-12 C²/J-m)(0.120 m)²)
= -3.6860e4 N/C, the negative sign means the electric field is in toward the sphere.

E = q / (4or²)
= -5.9e-8 C / (4(8.85e-12 C²/J-m)(0.120 m + 0.0700 m)²)
= -1.4703e4 N/C

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