Sketching Electric Field Lines of Circular Arc w/ Uniform Charge

[DWill]

Homework Statement

Sketch a field line picture for a circular arc with a uniform linear charge density.

Homework Equations

The Attempt at a Solution

To do this do I just break up each segment on the arc into small segments each of charge dQ and draw the field line along the electric field caused by each small segment? If so, assuming the charge is positive, on the "outside" of the arc does the field spread out pointing away from the arc, and on the inside does it seem to focus to almost a point (still pointing in direction away from arc)?
Thanks

 

[Badi]

Do you want the field lines in 3D or just in the plane of the arc?

 

[thomate1]

for your question. Drawing field lines for a circular arc with a uniform charge density is a great way to visualize the electric field in this scenario. You are correct in your approach - you can break up the arc into small segments and draw the field lines based on the electric field caused by each segment.

For a positive charge, the field lines will indeed spread out from the outside of the arc, pointing away from the arc. On the inside, the field lines will appear to focus towards a point, still pointing away from the arc. This is because the electric field is strongest at the edges of the arc, where the charge is more concentrated, and weaker towards the center where the charge is more spread out.

It may also be helpful to keep in mind that the electric field lines always point in the direction of the electric force that a positive test charge would experience. So in this case, a positive test charge placed at any point on the arc would experience a force pointing away from the arc, in the direction of the field lines.

I hope this helps with your sketching process. Keep in mind that the number of field lines drawn should be proportional to the amount of charge on the arc, and the spacing between the lines should be proportional to the strength of the electric field. Happy sketching!