Electric potential and Field Lines

• Sigmeth
In summary: What you have to do now is calculate the work done in moving a 1C positive charge from point A to point B. Do that by figuring out how much energy is needed to move the charge and multiplying that by the distance between the points.
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?

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?
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?

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.

Sigmeth said:
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.

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.

1. What is electric potential?

Electric potential is a measure of the potential energy per unit charge at a specific point in an electric field. It is also known as voltage.

2. How is electric potential different from electric field?

Electric field is a measure of the force per unit charge experienced by a charged particle in an electric field, while electric potential is a measure of the potential energy per unit charge at a specific point in an electric field.

3. How are electric potential and field lines related?

Electric field lines are used to represent the direction and strength of an electric field. The closer the lines are together, the stronger the electric field. Electric potential decreases in the direction of the electric field, so the field lines point in the direction of decreasing potential.

4. Can electric potential be negative?

Yes, electric potential can be negative. It is a relative measure and is defined as the difference in potential energy between two points. If the starting point has a higher potential energy than the end point, the electric potential will be negative.

5. How does distance affect electric potential?

Electric potential is inversely proportional to distance. This means that as distance increases, electric potential decreases. This can be seen in the equation V = kQ/r, where V is electric potential, Q is the magnitude of the charge, r is the distance, and k is a constant.

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