A solid insulating sphere of radius 5.00 cm is centered at the origin. It carrie

Question

A solid insulating sphere of radius 5.00 cm is centered at the origin. It carries a total charge of 2.00 C uniformly distributed through its volume. Concentric with this sphere is an uncharged conducting shell whose inner and outer radii are 8.00 cm and 10.0 cm respectively. What is the electric field (magnitude and direction) 1.00 cm from the origin How much charge resides on the inner surface of the conductor What is the electric field (magnitude and direction) 9.00 cm from the origin What is the potential (with respect to infinity) at the inner surface of the conducting sphere

Explanation / Answer

part A:

from gauss law

closed integral of E.dL = Qin/eo

here for r = 1 cm

Qin = 2C)r/R)^3

Qin = 2 * 1cm^3/5cm^3

Qin = 0.16 C

E = 0.16/(4pi 0.01^2 * 8.85 *10^-12)

E = 1.44 *10^-12 N/C

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part B :

Charge inside the inner surface = 2C

part C:

E = 2/(4pi r^2 * eo)

E = 2* 9E9 /(9E-2)^2   

E = 2.22 *10^12 N/C

part D:

E = -V/d

Vb - Vo = -E r

Va - Vb = Kq (2)/0.1

Va-Vb = (9E9 * 2/0.08) - ( 9E9 * 2/0.05)

= -1485 V

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