Question

A conducting spherical shell of inner radius R1 and outer radius R2 has a point charge +q located at its center. The spherical shell has a net charge of +aq
A) enter an expression for the surface charge density on the inner surface of the spherical shell

B) enter an expression for the surface charge density on the outer surface of the shell

C) the electic field at the surface points radially outward and has a magnitude of 9900N/C. If R1=0.5m, R2=1.1m, and a=3 what is q in coulombs?

Answer 1

Answer:

 

Explanation:

Given

Point charge q is placed at the center and a net charge of +a q is on the spherical shell.

Assuming a Gaussian surface $r>R_1$

$\oint E\cdot ds=\frac{Q_{net}}{\epsilon _0}$

$\oint E\cdot ds=\frac{q+\sigma _i\cdot 4\pi R_1^2}{\epsilon _0}$

where $\sigma _i=$surface charge density

Considering  a point where Electric field  is  zero  at distance r

$q+\sigma _i(4\pi R_1^2)$

$\sigma _i=\frac{-q}{4\pi R_1^2}$

(b)Net charge on the shell is a q

Net charge can be written as summation of inner charge+outer charge

$aq=q_i+q_o$

$aq=\sigma _i(4\pi R_1^2)+\sigma _o(4\pi R_2^2)$

$aq=-q+\sigma _o(4\pi R_2^2)$

$aq+q=\sigma _o(4\pi R_2^2)$

$\sigma _o=\frac{aq+q}{4\pi R_2^2}$

(c)If $E=9900\ N/C$

$R_1=0.5\ m$

$R_2=1.1\ m$

and $a=3$

$E=\frac{kQ}{R_2^2}$

$9900=\frac{9\times 10^9\times 3q}{1.1^2}$

$q=380.9\times 10^{-9}\ C$

$q=0.380\ \mu C$