Question

A −4.00 μC charge sits in static equilibrium in the center of a conducting spherical shell that has an inner radius 3.13 cm and an outer radius 4.13 cm. The shell has a net charge of −6.43 μC. Determine the charge on each surface of the shell and the electric field just outside the shell.

charge on inner surface of shell μC
charge on outer surface of shell μC
magnitude of electric field just outside the shell N/C

Answer 1

(a). The charge on the outer surface is −2.43 μC.

(b). The charge on the inner surface is 4.00 μC.

(c). The electric field outside the shell is
`3.39*10^(7)\ N/C`

Step-by-step explanation:

Given that,

Charge q₁ = -4.00 μC

Inner radius = 3.13 m

Outer radius = 4.13 cm

Net charge q₂ = -6.43 μC

We need to calculate the charge on the outer surface

Using formula of charge

`q_(out)=q_(2)-q_(1)`

`q_(out)=-6.43-(-4.00)`

`q_(out)=-2.43\ \mu C`

The charge on the inner surface is q.

`q+(-2.43)=-6.43`

`q=-6.43+2.43= 4.00\ \mu C`

We need to calculate the electric field outside the shell

Using formula of electric field

`E=(kq)/(r^2)`

Put the value into the formula

`E=(9*10^(9)*6.43*10^(-6))/((4.13*10^(-2))^2)`

`E=33927618.73\ N/C`

`E=3.39*10^(7)\ N/C`

Hence, (a). The charge on the outer surface is −2.43 μC.

(b). The charge on the inner surface is 4.00 μC.

(c). The electric field outside the shell is
`3.39*10^(7)\ N/C`