Electric Field Intensity due to an infinitely long straight uniformly charged wire

This the photo of my textbook, Here In the derivation of Electric Field Intensity due to an infinitely long straight uniformly charged wire - In the figure 1(c).20 Vector E1 and vector E2 are electric fields at point P due to the two line elements as shown in the figure 1(c).20. But, in this figure 1(c).20 two Electric field lines are shown intersecting PE1 and PE2, how can this be done as we know that Two electric field lines never intersect each other then how are they intersecting here....

If anyone wants to know what electric field lines are you can go here- https://byjus.com/physics/electric-field-lines/

• Regarding your question format, it's not good practice to post a photograph from a text book. That type of item cannot be indexed for search engines. There are several drawing programs that would produce a simple sketch, and you should type out any necessary text. Apr 4, 2021 at 15:13

The arrows in the diagram are not real electric field lines, but rather the contribution to the electric field given by the infinitesimal line elements PE1 and PE2. These can certainly intersect.

Electric field lines are something totally different from what is shown in the figure. For the infinite line coming out of the page it would look like:

It is true that two electric field lines never intersect, and indeed if one drew the electric field lines for the distribution they would point radially outwards, no intersection as needed.

• @ KoutaDagnin,Please tell me what do you mean by this-The arrows in the diagram are not real electric field lines, but rather the contribution to the electric field given by the infinitesimal line elements PE1 and PE2. These can certainly intersect.Please explain it more deeply. please,please.... Apr 4, 2021 at 15:19
• the arrows in the diagram you uploaded just show the direction of the contribution to the electric field due to the line elements PE1 and PE2. To find the field at P, you would have to sum over all the line elements in the line charge distribution. Repeat this process for all points P and you will find that none of the electric field lines intersect. Apr 4, 2021 at 15:49
• see the figure 1(c).20, The Electric field lines PE1 and PE2 due to the two line elements are intersecting but how can these electric field lines intersect, as we know that electric field lines do not intersect each other.then how the electric field lines are intersecting here.....You are saying-The arrows in the diagram are not real electric field lines. then what they are... please help me Apr 4, 2021 at 15:59
• they are components of the electric field, but they don't give the total electric field. Apr 4, 2021 at 16:04
• You mean PE1 and PE2 in the figure 1(c).20 are components of the electric field lines at P1 and P2 which are radial outward. Does this mean that the electric field lines components can intersect each other... Apr 4, 2021 at 16:07

They are showing electric field lines due to individual charge segments at different locations along the wire, not the net electric field due to the whole wire.

• My question is see the figure 1(c).20, The Electric field lines PE1 and PE2 due to the two line elements are intersecting but how can these electric field lines intersect, as we know that electric field lines do not intersect each other.then how the electric field lines are intersecting here... Apr 4, 2021 at 16:01
• @Shashwatsingh And that's exactly what I answered! Electric field lines due to individual charges are NOT the total field. It's the total electric field which give lines that don't cross. Apr 5, 2021 at 2:07

What is meant with that picture is simply that the electric field lines $$E_1$$ and $$E_2$$ that the individual positive charged particles $$P_1$$ and $$P_2$$ create (representing each electric fieldline from each charged particle of the charged surface) cancel each other out tangentially. This results in an overall electric field $$E$$ that is orthogonal to the positive charged surface. The fact that fieldlines don't overlap each other only applies to this overall electric field, as the idea behind it, is the overall electric field being unique in every point in space.

That's a terrible illustration.

Those lines are neither field lines nor vectors. Those lines having arrows at the end don't represent anything. I will give the author the benefit of the doubt and suppose that he or she intended to display vectors anchored at the point of interest. The lines below the dotted line are perhaps to display the length and direction of the field point with respect to the charge element. The two should be differentiated somehow, perhaps by making one a dotted line, or a different color line.

• my question is see the figure 1(c).20, The Electric field lines PE1 and PE2 due to the two line elements are intersecting but how can these electric field lines intersect, as we know that electric field lines do not intersect each other.then how the electric field lines are intersecting here... Apr 4, 2021 at 16:00
• Each line has a different charge element as it's source. The individual field lines from each separately can intersect. The field lines due to the sum cannot intersect. Still, that illustration is really confusing. Those lines are a confusing pile of crap. Apr 5, 2021 at 2:20