A nonconducting sphere is made of two layers. The innermost section has a radius of 6.0 cm and a uniform charge density of −5.0C/m^3. The outer layer has a uniform charge density of +8.0C/m^3 and extends from an inner radius of 6.0 cm to an outer radius of 12.0 cm. Find the total charge Q on the sphere.

The total charge on the sphere is 46.11 x 10⁻³ C

Explanation:

Given:

charge density of innermost section, σ = −5.0C/m³

radius of the innermost section, r = 6.0cm

charge density of the outer layer ,σ = +8.0 C/m³

radius of the outer layer, r =12.0cm

volume of sphere is given as

Charge enclosed by the innermost section = volume x charge density

volume

Enclosed charge, q₁ = −5.0C/m³ X 9.05 x 10⁻⁴ m³

                             = - 4.53 x 10⁻³ C

Charge at the outer surface

Volume =  

Enclosed charge, q₂ = +8.0 C/m³ X 0.00633 m³

                            = 50.64 x 10⁻³ C

Total charge on the sphere; Q = q₁ + q₂

                                                   = - 4.53 x 10⁻³ C +  50.64 x 10⁻³ C

                                                   =  46.11 x 10⁻³ C

Therefore, the total charge on the sphere is 46.11 x 10⁻³ C

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