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

Answer:

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

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 :

$E=\dfrac{kq}{r^2}$

$\dfrac{E_1}{E_2}=\dfrac{r_2^2}{r_1^2}$ (as electric field is inversely proportional to the distance)

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

$E_2=\dfrac{r_1^2}{r_2^2}E_1$

$E_2=\dfrac{0.22^2}{0.584^2}\times 430$

$E_2=61.02\ N/C$

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.