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A metallic sphere centered at the origin has density of 24.6nC/m^2. In r=2 the potential is...

A metallic sphere centered at the origin has density of 24.6nC/m^2. In r=2 the potential is 500V and the magnitude of the electrical field is 250 V/m. Determine the radius of the sphere.

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Answer #1

Applying Gauss law

=> E * A = Q/eo

where, E * A =   250 * 3.14 * 2 * 2

                     = 3140 V.m

=> Q = 3140 * 8.854 * 10-12

           = 2.78 * 10-8 C

As, Q = ρ * A

=>    2.78 * 10-8 = 24.6 * 10-9 * 3.14 * R2

=>   R = 0.6 m

Thus, the radius of the sphere = 0.6 m

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