# Inferring charge via electric field properties

1. Oct 5, 2009

### phil ess

1. The problem statement, all variables and given/known data

You are 1.5m from a charge distribution whose size is much less than 1m. You measure an electric field strength of 282 N/C. You move to a distance of 2m, and the field strength becomes 119 N/C. What is the net charge of the distribution? HINT: Don't try to calculate the charge. Determine instead how the field decreases with distance, and from that infer the charge.

2. Relevant equations

E = kq/r2

3. The attempt at a solution

Well the electric field strength doesn't fall off as 1/r2, because if we calculate q for 1.5m using simple substitution, then use that q at 2m, I dont get the electric field given.

How do I figure out the field? If Im thinking graphically, I have two points (1.5,282) (2,119) and I have to find a curve that crosses those two points, a curve that describes how the electric field falls off.

I think the problem Im having here is that Im rusty on the math. I have a feeling that it would help to differentiate E = kq/r2 to perhaps be able to describe how the field is changing:

E' = -2kq/r3 But Im not sure how to use the given points to help...

E2/E1 = 0.422
r2/r1 = 4/3

Any hints would be appreciated!

2. Oct 5, 2009