Athin 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

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. dA = / 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 = / ε₀

The area of a sphere is

     A = 4π r²

    E 4π r² = / 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

    =  Eo /1.56 ²

   = 0.41 Eo

C) r = 2R

All charge inside is inside the Gaussian surface

    =(1 /4π ε₀ ) Q    1/(2R)²

    = (1 /4π ε₀ ) q/R²   1/4

    = Eo  1/4

    = 0.25 Eo

D) False the field changes with distance

The correct answer is B

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