A solid nonconducting sphere has a radius of 50.0 cm. It has a uniform charge de

Question

A solid nonconducting sphere has a radius of 50.0 cm. It has a uniform charge density of 3.00×10-3 C/m3. What is the strength of the electric field (a) at a distance of 2.00 m from the center of the sphere? (b) at the surface of the sphere? (c) at a distance of 25.0 cm from the center of the sphere? (Hint: use the shell theorem, which states that when calculating an electrostatic force or field outside a sphere with a uniform charge, the sphere can be treated as though all of its charge resides at the center.)

*Please give details on the steps used to find the answer.

Explanation / Answer

Given

radius of the sphere r = 50 cm = 0.5 m

charge density = 3*10-3 C / m3  

                      q / A =   3*10-3 C / m3  

charge inside the sphere q = (3*10-3 C / m3  )( 0.52 )

                                         = 2.35mC

Electric field at a distance 2m from the center of the field

               E = k q / r 2

                   = ( 9*109 )(2.35*10-3 C ) / ( 4)

                    = 5.301*106 N / C  

Electric field at the surface of the sphere

             E = k q / r 2

                   = ( 9*109 )(2.35*10-3 C ) / ( 0.5)2

                  = 8.46*107 N / C  

electric field at a distance 25 cm from the center of the sphere

            E = k q / r 2

                   = ( 9*109 )(2.35*10-3 C ) / ( 0.25)2

                  = 3.384*107 N / C

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