Question

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.

Answer 1

Answer:

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 $= \frac{4}{3}.\pi r^3$

Charge enclosed by the innermost section = volume x charge density

volume $= \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (0.06^3) = 9.05 X 10^{-4} m^3$

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 =  $\frac{4}{3}\pi [r_2{^3} - r_1{^3}] = \frac{4}{3}\pi [0.12{^3} - 0.06{^3}] = 0.00633 {m^3}$

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