# Electric Field of a Conducting Sphere

## Homework Statement

At a distance of 0.206cm from the center of a charged conducting sphere with radius 0.100cm, the electric field is 485N/C . What is the electric field 0.612cm from the center of the sphere?

## Homework Equations

E(r)=1/4∏ε_0 * qr/R^3
where r is radius of the Gaussian surface and R is the radius of the sphere

## The Attempt at a Solution

I tried this two different ways, and they were both the same answer (and both wrong). Firstly, I used the given E-field (485N/C) and plugged it in to the above equation and solved for q. Once I solved for q, I used that q with a new distance from the center of the sphere to solve for the new E Field at that position. When I did that, I got that the electric field should equal 1440.874 N/C. I plugged this in to my online homework site, and it said I was wrong.

Since that way seemed to be wrong, I tried to just set it up as a ratio. I said that:

(485N/C)/0.00206m = (x N/C)/.00612m

Solving for x, which represents the E Field, I again got 1440.874 N/C.

Any ideas where I might have gone wrong?

## Homework Statement

At a distance of 0.206cm from the center of a charged conducting sphere with radius 0.100cm, the electric field is 485N/C . What is the electric field 0.612cm from the center of the sphere?

## Homework Equations

E(r)=1/4∏ε_0 * qr/R^3
where r is radius of the Gaussian surface and R is the radius of the sphere

Does this formula apply to the field outside the sphere?

I tried this two different ways, and they were both the same answer (and both wrong). Firstly, I used the given E-field (485N/C) and plugged it in to the above equation and solved for q.

How? Using the formula above?

(485N/C)/0.00206m = (x N/C)/.00612m

Is electric field inversely proportional to distance?