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/m3. The outer layer has a uniform charge density of +8.0C/m3 and extends from an inner radius of 6.0 cm to an outer radius of 12.0 cm.

A) Determine the electric field for 0
B) Determine the electric field for 6.0cm
C) Determine the electric field for 12.0cm

a) E =0, b)   E = 1,129 10¹⁰ N / C , c)    E = 3.33 10¹⁰ N / C

Explanation:

To solve this exercise we can use Gauss's law

        Ф = ∫ E. dA = / ε₀

Where we must define a Gaussian surface that is this case is a sphere; the electric field lines are radial and parallel to the radii of the spheres, so the scalar product is reduced to the algebraic product.

           E A = /ε₀

The area of a sphere is

          A = 4π r²

         E = q_{int} / 4πε₀ r²

         k = 1 / 4πε₀

         E = k q_{int} / r²

To find the charge inside the surface we can use the concept of density

        ρ = q_{int} / V ’

         q_{int} = ρ V ’

         V ’= 4/3 π r’³

Where V ’is the volume of the sphere inside the Gaussian surface

 Let's apply this expression to our problem

a) The electric field in center r = 0

     Since there is no charge inside, the field must be zero

          E = 0

b) for the radius of r = 6.0 cm

In this case the charge inside corresponds to the inner sphere

        q_{int} = 5.0  4/3 π 0.06³

         q_{int} = 4.52 10⁻³ C

        E = 8.99 10⁹  4.52 10⁻³ / 0.06²

         E = 1,129 10¹⁰ N / C

c) The electric field for r = 12 cm = 0.12 m

In this case the two spheres have the charge inside the Gaussian surface, for which we must calculate the net charge.

     The charge of the inner sphere is q₁ = - 4.52 10⁻³ C

The charge for the outermost sphere is

       q₂ =  ρ 4/3 π r₂³

       q₂ = 8.0 4/3 π 0.12³

       q₂ = 5.79 10⁻² C

The net charge is

     q_{int} = q₁ + q₂

     q_{int} = -4.52 10⁻³ + 5.79 10⁻²

     q_{int} = 0.05338 C

The electric field is

        E = 8.99 10⁹ 0.05338 / 0.12²

        E = 3.33 10¹⁰ N / C

answer: the direction of the wind is expressed as the direction from which the wind is blowing. for example, easterly winds blow from east to west, while westerly winds blow from west to east.

explanation: