Question

A charge of q = +10-6 C is uniformly distributed on a spherical shell of radius 18 cm.
(a) What is the magnitude of the electric field just outside and just inside the shell?
_______ kV/m (outside)
________ kV/m (inside)

(b) What is the magnitude of the electric potential just outside and just inside the shell?
______V (outside)
_______V (inside)

(c) What is the electric potential at the center of the shell?
_____ V
What is the electric field at that point?
_____ kV/m

Answer 1

E=(1/4πε₀) (q/r²)

and,

V=(1/4πε₀) (q/r)

given,

r=18

for inside, R=r-d

for outside, R=r+d

1/4πε₀ = 9x10⁹ (conventional)

Answer 2

   Given
radius of the spherical shell   R = 18 cm = 0.18 m
   charge on the shell     q =1μ C = 1 *10^-6 C
(a) magnitude of electric field at just out side the shell,
            E = ( 1 / 4πε_o ) (q / R²)
                 = ( 9*10⁹) ( 1 *10^-6 C)/(0.18)^2
                 = 277.77 kV/m
    magnitude of electric field at just in side,
E = 0
there is no electric field inside the shell.

(b) the magnitude of the electric potential at just out side,
    V = ( 1 / 4πε_o ) (q / R)
         = ( 9*10⁹) ( 1 *10^-6 C)/(0.18)
          = 50 *10^3 V (out side)
the magnitude of the electric potential at just inside,
    V = ( 1 / 4πε_o ) (q / R)
         = ( 9*10⁹) ( 1 *10^-6 C)/(0.18)
          = 50 *10^3 V (inside)
(c) the electric potential at the center of the shell is zero.
        i.e V = 0 V
the electric field,
   E = 0 V/m