Drawing Electric Field Lines and Equipotential Lines

In summary, the task was to draw electric field lines and equipotential lines between two metal electrodes, one in the shape of a circle and one in the shape of a thin plank. The plank was at a lower electric potential and the circle at a higher potential. The circle was treated as positive and the plank as negative, with the E field lines emerging perpendicular to the surface of each electrode. The equipotential lines around the circle followed the shape of the electrode, while the ones around the plank appeared elongated and close together at the corners due to the strong E field.
  • #1
jumbogala
423
4

Homework Statement


You have two metal electrodes, not touching each other. One is a circle and one is like a thin plank. The plank is at a lower electric potential.

Draw electric field lines between them, including direction.

Draw equipotential lines in the space between the electrodes as well.


Homework Equations





The Attempt at a Solution


I'm not sure how to do this because I've never drawn electric field lines for things that are not just charged objects. What does the circle being at a lower potential tell you?

Does it mean that one object will act like a negative charge and the other like a positive charge?

Let's start with that because once I can draw the electric field lines, I think I can draw the equipotential lines (just 90 degrees everywhere to the field lines).
 
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  • #2
Yes, the one with the higher potential is positive with respect to the one with the lower potential. Remember that E field lines generally emerge perpendicular to the surface of the electrode.
 
  • #3
So what I'll do is treat the circle electrode as positive and the plank electrode as negative.

The only problem now is figuring out how the electric field lines from each object interact with each other. I can draw them for each object separately, but in the space right between the two objects I'm not sure. Just gradually change the field lines from one type to the other?

Would the charges have equal magnitudes (but opposite signs)?
 
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  • #4
Gradual is good, but the basic idea is to draw lines from the circle to the plank. Start with one going straight from the closest point on the circle to the middle of the plank. The others will tend to bulge out as they leave the circle perpendicular to its surface.
 
  • #5
So it should look similar to how 2 point charges would look, then.

Thanks, I think I can do it now!
 
  • #6
I finished drawing it. It seems like the equipotential lines should mimic the shape of the electrode.

The equipotential lines around the circle do, but not around the plank. The ones around the plank look like really elongated ovals: is that okay or should it be more rectangular?
 
  • #7
I'm not sure about the plank. It does seem to me that the lines should emerge perpendicular to it. The E field will be particularly strong at the corners, so the lines will be close together there.
 

Related to Drawing Electric Field Lines and Equipotential Lines

1. What is the purpose of drawing electric field lines and equipotential lines?

The purpose of drawing these lines is to visualize the electric field and potential in a given region, as well as to understand the interactions between charges and their effects on the surrounding space.

2. How are electric field lines and equipotential lines related?

Electric field lines and equipotential lines are perpendicular to each other at every point. This means that wherever an electric field line crosses an equipotential line, the electric field is acting in the direction of the equipotential line.

3. What do the spacing and direction of electric field lines represent?

The spacing of electric field lines represents the strength of the electric field, with closer lines indicating a stronger field. The direction of the lines indicates the direction in which a positive test charge would move when placed in the field.

4. How do equipotential lines help in understanding electric fields?

Equipotential lines are a visual representation of regions where the electric potential is constant. They help in understanding electric fields by showing that the electric field is always perpendicular to these lines, and that work done by the field depends only on the endpoints of the path taken.

5. Can electric field lines and equipotential lines intersect?

No, electric field lines and equipotential lines cannot intersect. If they were to intersect, it would mean that the electric field would have two different directions at the same point, which is not possible.

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