A charged metallic sphere, whose radius is 10 cm, is placed with its centre at t

Question

A charged metallic sphere, whose radius is 10 cm, is placed with its centre at the origin. The electric potential at the surface of the sphere is +100V.

a) what is the value of the electric potential at the origin (i.e., at the centre of the sphere)?

b) what is the electric field at the origin (i.e., at the centre of the sphere)?

c) What is the electric field at point P (which is at the surface of the sphere [point P is 450 above +x axis placed on the surface of the sphere in the xy plane)

Please do not only answer with numbers, I want to understand what is going on. As much detail as possible please!

Thank you

Explanation / Answer

The potential anywhere inside the sphere, including the origin, is 100V. That is because it is a conducting sphere and potential is everywhere the same, otherwise current would flow.

The electric field anywhere inside, including the origin, is zero. Electric field exists when there is a difference in potential .. constant potential equals zero electric field and vice versa.

To solve part c, consider that V = kq/r and E = kq/r2.   So E = V/r and if we do that calculation at the surface, we get E = (100 v) / (0.1 m) = 1000 v/m.

Since this is a sphere and is symmetrical, the electric field is the same anywhere on the surface, including your point P.

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