Question

A thin spherical shell of radius R has a total charge +Q uniformly distributed over its surface. Of the following distance r from the center of the sp , herical shell, which location has the greatest electric field strength?
(A) r = 3R/4
(B) r = 5R/4
(C) r = 2R
(D) None of the above because the field is of constant strength

Answer 1

Answer:

The correct answer is B

Explanation:

Let's calculate the electric field using Gauss's law, which states that the electric field flow is equal to the charge faced by the dielectric permittivity

         Φ$._{E}$ = ∫ E. dA = $q_{int}$ / ε₀

For this case we create a Gaussian surface that is a sphere.  We can see that the two of the sphere and the field lines from the spherical shell grant in the direction whereby the scalar product is reduced to the ordinary product

        ∫ E dA = $q_{int}$ / ε₀

The area of ​​a sphere is

     A = 4π r²

   

    E 4π r² =$q_{int}$ / ε₀

    E = (1 /4πε₀ )  q / r²

Having the solution of the problem let's analyze the points:

A   ) r = 3R / 4  = 0.75 R.

  In this case there is no charge inside the Gaussian surface therefore the electric field is zero

        E = 0

B) r = 5R / 4 = 1.25R

In this case the entire charge is inside the Gaussian surface, the field is

    E = (1 /4πε₀ )  Q / (1.25R)²

    E = (1 /4πε₀ )  Q / R2 1 / 1.56²

    E₀ = (1 /4π ε₀ )  Q / R²

   $E_{B}$ =  Eo /1.56 ²

  $E_{B}$  = 0.41 Eo

C) r = 2R

All charge inside is inside the Gaussian surface

    $E_{B}$ =(1 /4π ε₀ ) Q    1/(2R)²

    $E_{B}$ = (1 /4π ε₀ ) q/R²   1/4

    $E_{B}$ = Eo  1/4

    $E_{B}$ = 0.25 Eo

D) False the field changes with distance

The correct answer is B