A solid conducting sphere of radius 200 cm has a charge 890

A solid conducting sphere of radius 2.00 cm has a charge 8.90 µC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a charge -3.40 µC. Find the electric field at the following radii from the center of this charge configuration.

(a) r = 1.00 cm
1 N/C
(b) r = 3.00 cm
2 N/C
(c) r = 4.50 cm
3 N/C
(d) r = 7.00 cm
4 N/C

Solution

a) zero

here is no charge inside of a solid conductor

-------------------------------------------------

b) r = 3.00 cm

E = Q / 4 * pi * epsilon₀ * r²

= (8.9 * 10^-6 C) / ( 4 * 3.14 * 8.85 * 10-12 * (3.00 * 10^-2 )² )

= 88.9 MN/C

------------------------------------------------

c) zero

-----------------------------------------------

d) r = 7.00 * 10^-2 m , q₁ = 8.90 * 10^-6 C , q₂ = -3.40 * 10^-6 C

E_net = E_inner + E_outer = [Q_inner + Q_outer] / [4 * pi * epsilon₀ * r²]

= [(8.90 * 10^-6 ) - (3.40 *10^-6 )] / [4 * pi * 8.85 * 10^-12 * (7.00 * 10^-2 m)² ]

= 10.1 MN/C