Charge vs. Electric Field Strength

[Sperry]

The question in question:
"If charge was plotted versus electric field strength; what shape of graph would you get? How would you straighten in? What quantity would the slope of the straightened graph represent?"

Related equation: |E|= F/q

Ignoring the graphing information, the question (as far as I gather) seems to be asking me to rearrange for q/|E|.

Now,
|E|q = F
q = F/|E|
q/|E| = F/|E|^2
From that, plotting charge versus field strength results in Force versus the square of the field strength. Which doesn't seem very helpful at all. The units there are C/(N/C), or C^2/N.

So, my issue: Am I going about this in the right way? If so, where do I go from here? Does C^2/N represent anything of worth?

At a bit of a loss here, so any help would be greatly appreciated.

 

[rock.freak667]

The question in question:
"If charge was plotted versus electric field strength; what shape of graph would you get? How would you straighten in? What quantity would the slope of the straightened graph represent?"

I think this is asking what you would plot so that the graph becomes a straight line.

You are correct in saying that $E=\frac{F}{Q}$ If you re-arrange for Q, you get
$Q = \frac{F}{E}$

How would you put that in the form Y=MX+C to get it into a straight line?

 

[Moetasim]

Thanks!

The graph you would get when plotting charge versus electric field strength would depend on the distribution of charge and the type of material in the electric field. In general, the relationship between charge and electric field strength is not a simple one and cannot be represented by a single graph.

However, if we assume a uniform electric field and a point charge, the graph would show a linear relationship between charge and electric field strength. The slope of this straight line would represent the inverse of the electric field strength, or 1/|E|. This quantity is known as the electric permittivity of the material and is a measure of how easily the material can be polarized by an electric field.

To straighten the graph, we would need to plot 1/|E| versus charge. This would result in a straight line with a slope equal to the permittivity of the material. The units of this quantity would be C^2/(N*m^2), which represents the amount of charge that can be stored per unit area in the material when subjected to an electric field.

In summary, the slope of the straightened graph represents the electric permittivity of the material, which is a measure of how easily it can be polarized by an electric field. This quantity has practical applications in the design of capacitors and other electrical devices. However, it is important to note that this relationship is only valid for simple cases and may not apply to all materials and distributions of charge.