Question

At a distance of 0.220 cmcm from the center of a charged conducting sphere with radius 0.100cm0.100cm, the electric field is 430 N/CN/C . What is the electric field 0.584 cmcm from the center of the sphere?

Answer 1

The electric field at a distance of 0.584 cm from the center of the sphere is 61.02 N/C.

Step-by-step explanation:

Given that,

Initial distance,
`d_1=0.22\ cm`

Initial electric field,
`E_1=430\ N/C`

We need to find the electric field 0.584 cm from the center of the sphere,
`d_2=0.584\ cm`. The electric field at a distance d is the given by :

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

`(E_1)/(E_2)=(r_2^2)/(r_1^2)` (as electric field is inversely proportional to the distance)

`E_2` is the electric field 0.584 cm from the center of the sphere

`E_2=(r_1^2)/(r_2^2)E_1`

`E_2=(0.22^2)/(0.584^2)* 430`

`E_2=61.02\ N/C`

So, the electric field at a distance of 0.584 cm from the center of the sphere is 61.02 N/C. Hence, this is the required solution.