Question

A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 18.0 cm , giving it a charge of-29.0 μC .

A Find the electric field just inside 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.

Answer 1

Using Gauss's law, the electric field just inside a uniformly charged spherical layer is found with the formula E = Q / (4πε0r2). For a sphere with a -29.0 μC charge, the field is directed radially inward.

Step-by-step explanation:

To find the electric field just inside the paint layer of a charged spherical object, we use Gauss's law. For a charged sphere, the electric field E inside a uniformly charged surface is given by the expression E = Q / (4πε0r2), where Q is the total charge, ε0 is the permittivity of free space (8.854 x 10-12 C2/Nm2), and r is the radius of the sphere. In this case, the sphere's diameter is 18.0 cm, so the radius r is 9.0 cm or 0.09 m, and the charge Q is -29.0 μC or -29.0 x 10-6 C. Plugging these values into the formula we get:

E = (-29.0 x 10-6 C) / (4π x 8.854 x 10-12 C2/Nm2 x (0.09 m)2)

After calculating, we find the magnitude of the electric field and note that the field is directed radially inward (since the charge is negative), so the electric field 'E' has a positive value.