To find the net charge of distribution

[hoycey]

Homework Statement

You're 1.5 m from a charge distribution whose size is much less than 1 m.
You measure an electric field strength of 282 N/C. You move to a distance of
2.0 m, and the field strength becomes 119 N/C.

Hint: Don't try to calculate the charge. Instead determine how the field
decreases with distance and from that, infer the charge.

Homework Equations

The Attempt at a Solution

All I was taught by the prof was that I need to break charge distribution
into elements of dq and then integrate over the distance. However, the
question does not necessarily state the distance of the distribution, which is
why I think the question gives two instances of field measurements, I'm not
sure how to approach the question from here. Hope that I can get a good
lead on how to solve this question. Thanks.

 

[diazona]

What does the question ask you to figure out?

 

[hoycey]

Hi, the question asks to find the net charge of the distribution

 

[gabbagabbahey]

Hint: Since the charge distribution is much less than 1m in size, and the field is measured at points further away than one meter, you are effectively far away from the charge distribution...what terms in the field's multipole expansion do you expect to dominate when you are far away from the charge distribution?

 

[FlightCapt]

I think what you're looking for has something to do with the inverse cube of the distance between the charge distribution and the point where you are measuring. As to the net distribution...I'm still unclear how to infer that unless it's infinite ( ie. 1/0^3 when you're measuring at the charge distribution) but it doesn't make sense physically I think.

 

[gabbagabbahey]

I think what you're looking for has something to do with the inverse cube of the distance between the charge distribution and the point where you are measuring. As to the net distribution...I'm still unclear how to infer that unless it's infinite ( ie. 1/0^3 when you're measuring at the charge distribution) but it doesn't make sense physically I think.

This thread is almost a year-old, I doubt the OP is still working on the problem.

Anyways, the point is that the electric field of any charge distribution can be expanded in a so-called multipole expansion... there will be terms that are proportional to $\frac{1}{r^2}$ (monopole term) $\frac{1}{r^3}$ (dipole term) and so on. When you are "far" from the distribution, only the first 2 or 3 terms will be significant, so in this case, you assume only a monopole and dipole terms are present and use the given information to find the coefficients of each...the coefficient of the monopole moment is directly proportional to the total charge of the distribution.