A thin spherical shell with radius R1 = 4.00 cm is concentric with a larger thin spherical shell with radius 7.00 cm. Both shells are made of insulating material. The smaller shell has charge q1 = +6.00 nC distributed uniformly over its surface, and the larger shell has charge q2 = -9.00 nC distributed uniformly over its surface. Take the electric potential to be zero at an infinite distance from both shells. A. What is the electric potential due to the two shells at the following distance from their common center: r= 0? B. What is the electric potential due to the two shells at the following distance from their common center: r= 5.00 cm? C. What is the electric potential due to the two shells at the following distance from their common center: r= 8.00 cm? D. What is the magnitude of the potential difference between the surfaces of the two shells? E. Which shell is at higher potential: the inner shell or the outer shell?

a) ΔV = 0 , b)    ΔV = 1.08 10² V , c)  ΔV = -5,394 10¹ V, d) ΔV = 5.394 / r                 4 <r <7 , e) ΔV₂ = 1,156 10²  V    The outer sphere has greater potential

Explanation:

The electrical potential can be calculated

          ΔV = - ∫ E. ds

-Within a conductive body the electric potential and the electric field are zero

-Conductive surface strength in electric field is

          ΔV = -∫ E .ds

          ΔV = -∫ k Q / r² dr

          ΔV = k Q / r

Let's apply this to our case

A) distance r = 0

     Since all equipotential surfaces are external, the electrical potential is

               ΔV = 0

B) the distance of r = 5 cm

In this case the tip is inside the outer sphere, which is why it gives a contribution to the potential of zero

The point is outside the small sphere, so the power is

                 ΔV = k Q₁ / r

                 ΔV = 8.99 10⁹ 6 10⁻⁹ / 5 10⁻²

                 ΔV = 1.08 10² V

C) distance r = 8.00 cm

In this case, the point is outside the two spheres, so both contribute to the potential

                 ΔV = k q₁ / r + k q₂ / r

                 ΔV = 8.99 10⁸ (6 -9) 10⁻⁹ / 5 10⁻²

                 ΔV = -5,394 10¹ V

D) the potential between the two spheres is created by the inner sphere only

               ΔV = K q₁ / r                    4 <r 7

               ΔV = 8.99 10⁸ 6 10⁻⁹ / r

               ΔV = 5.394 / r                 4 <r <7

E) The potential of the inner sphere is

               ΔV₁ = 8.99 10⁸ 6 10⁻⁹ / 5 10⁻²

               ΔV₁ = 1.0788 10² V

Potential of the outer sphere

                ΔV₂ = 8.99 10⁸ 9 10⁻⁹ / 7 10⁻²

                ΔV₂ = 1,156 10²  V

The outer sphere has greater potential

it is a negative acceleration

490 n

f=125n a=2.5m/s2