Question

Two charged concentric spherical shells have radii of 11.0 cm and 14.0 cm. The charge on the inner shell is 3.50 ✕ 10−8 C and that on the outer shell is 1.60 ✕ 10−8 C. Find the magnitude of the electric field at the following points.

Answer 1

The magnitude of the electric field are
`2.38*10^(4)\ N/C` and
`1.09*10^(4)\ N/C`

Step-by-step explanation:

Given that,

Radius of inner shell = 11.0 cm

Radius of outer shell = 14.0 cm

Charge on inner shell
`q_(inn)=3.50*10^(-8)\ C`

Charge on outer shell
`q_(out)=1.60*10^(-8)\ C`

Suppose, at r = 11.5 cm and at r = 20.5 cm

We need to calculate the magnitude of the electric field at r = 11.5 cm

Using formula of electric field

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

Where, q = charge

k = constant

r = distance

Put the value into the formula

`E=(9*10^(9)*3.50*10^(-8))/((11.5*10^(-2))^2)`

`E=2.38*10^(4)\ N/C`

The total charge enclosed by a radial distance 20.5 cm

The total charge is

`q=q_(inn)+q_(out)`

Put the value into the formula

`q=3.50*10^(-8)+1.60*10^(-8)`

`q=5.1*10^(-8)\ C`

We need to calculate the magnitude of the electric field at r = 20.5 cm

Using formula of electric field

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

Put the value into the formula

`E=(9*10^(9)*5.1*10^(-8))/((20.5*10^(-2))^2)`

`E=1.09*10^(4)\ N/C`

Hence, The magnitude of the electric field are
`2.38*10^(4)\ N/C` and
`1.09*10^(4)\ N/C`