Electric potential and Field Lines

[Sigmeth]

Sorry for any errors in posting, this is my first thread. Any help would be greatly appreciated!

Homework Statement

a.)On the contour map that is attached, find the magnitude of the electric field at each point A, B, and C.
b.)Calculate the work done in moving a 1C positive charge from point A to point B.

Homework Equations

For a.) E=dV/dx Change in potential between bounding equipotential lines/length of the line between bounding equipotentials.
For b.) W=qΔV

The Attempt at a Solution

For a.) I can find the electric fields at points A and B, but I am not sure how to find point C. Since it is surrounded by the 180, does this mean the magnitude of the electric field at point C is zero? Also, I am not sure the direction of the electric field at point C. I know it is from high potential to low potential.
For b.) Using W=qΔV, I have W=(1C)(180-170). I feel as though I am way off. Does it matter that the lines are not uniform?

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Simon Bridge]

For a.) I can find the electric fields at points A and B, but I am not sure how to find point C. Since it is surrounded by the 180, does this mean the magnitude of the electric field at point C is zero?

Treat it like a geography contour map - would you expect point C to be on top of a hill?
I think this is a judgement call - whatever you decide, you'll have to justify it with some kind of argument.

Also, I am not sure the direction of the electric field at point C. I know it is from high potential to low potential.

If the magnitude is zero - does it matter?
If it is not, then the direction is towards the nearest lower potential line.
To see what I mean - try sketching in equipotential lines for 182 and 184 and 186 Volts.

For b.) Using W=qΔV, I have W=(1C)(180-170). I feel as though I am way off. Does it matter that the lines are not uniform?

Consider - the electric field is conservative. What does that mean about the path you choose?

 

[Sigmeth]

I guess the issue I am having with C is that I need to examine the magnitudes of the electric fields at each point to determine a convenient scale to show the electric fields as vectors on the map (This is my fault in not including in the original problem). This is why I am having issues with the magnitude at point C being zero. I have for point A, (170-160)/1.2= 8.3. Point B I have (190-180)/0.5= 20. (Both answers being in V/cm).---I am assuming that the magnitude for C equals zero because the field line does not increase past 180 (Like being on top of a hill). So the issue I am having is that any convenient scale I draw for V/cm will contradict any line I draw for the electric field for point C.

As for part B, I am thinking that the fact that the lines are not uniform does not matter since the electric field is conservative.

 

[haruspex]

As for part B, I am thinking that the fact that the lines are not uniform does not matter since the electric field is conservative.

Yes, but I don't think your 180-170 is quite right. Looks to me that each is about half way between two contour lines.

 

[Simon Bridge]

to determine a convenient scale to show the electric fields as vectors on the map

You don't have to draw the vectors to scale.

I am assuming that the magnitude for C equals zero because the field line does not increase past 180

You don't know that though do you - since the next equipotential line is drawn at 190 ... all you know is that the hill does not climb as high as that. It could peak at, say, 189 ... or, it could be that the 180 line around point C is the highest ridge and there is a shallow crater there that goes as low as 171 (say). You need to use your understanding of electric charges to figure out what is likely - but you still have to make a guess.

For part (b) - consider that you have figured out the potential at points A and B in part (a) and how, the field being conservative, the path you choose from A to B affects the amount of work needed.