# Electric potential and Field Lines

by Sigmeth
Tags: electric, field, lines, potential
 P: 2 Sorry for any errors in posting, this is my first thread. Any help would be greatly appreciated! 1. The problem statement, all variables and given/known data 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. 2. Relevant equations For a.) E=dV/dx Change in potential between bounding equipotential lines/length of the line between bounding equipotentials. For b.) W=qΔV 3. 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? 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
HW Helper
Thanks
P: 9,101
 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?
 P: 2 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.
HW Helper
Thanks
P: 7,919

## Electric potential and Field Lines

 Quote by Sigmeth 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.
HW Helper