Electricity and magnetism confusion

[Dongorgon]

Homework Statement

I've been set an assignment and I'm struggling with one question in particular:

Homework Equations

'Use the following data and plot the graphs for a point charge'

'Plot graph of E against r^2. Interpret the graph to describe electric field strength and electric potential.'

The figures provided are r(m)=Distance from a point charge, and, V(V)=Voltage at a distance 'r' from a point charge.

The Attempt at a Solution

More than anything I'm just really stuck how to find E from the figures provided? Any help would be greatly appreciated! Thanks

 

[cosmic dust]

The filed at r=r_i wil be:
E = -dV/dr ≈ -ΔV_i/Δr_i
where ΔV = V(r_i+1)-V(r_i) and Δr_i = r_i+1-r_i

 

[HallsofIvy]

I don't see how it would be possible to answer this without knowing what data you are given!

 

[Dongorgon]

Apologies, the date given is as follows:

R(m)=Distance from point charge:

0.0254
0.0508
0.05762
0.1016
0.127
0.1524
0.1778

And corresponding respectively, the V(V)=VOltage at a distance 'r' from a point charge:

236.22
214.57
157.58
108.03
94.48
85.3
73.11

 

[gneill]

You're told that the given data corresponds to potential U at distances r from a point charge. What expressions do you know that correspond to electric potential U and electric field E at distance r from a point charge?

 

[Dongorgon]

Ok, so from equations to give V and E, I've come up with this as a potential solution for the first E value from the first two values of distance and voltage. Is this correct?

 

[gneill]

No need to plug in numerical values yet; you have a whole table full of values to plot later. Just write the expressions for potential and electric field for a point charge. Solve the potential expression for Q and substitute it into the field expression. That'll leave you with an expression for E involving only V and r. You can plot that since you have a table full of values for V and r.

(as an aside, note that electric field strengths are given in V/m or N/C, not Teslas which are a measure of magnetic field strength)

 

[Dongorgon]

Brilliant, piece of cake. Many thanks to those who have helped!