# Is this property of lines of force true for E.M?

## Main Question or Discussion Point

Considering the visual representation of an electric/magnetic field (by 'line of forces'), is this fact about the properties of lines of force true? -

"Each line of force has equal strength"

The websites/books are pretty timid in reviling the properties of lines of forces...at least for E.Fs.

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Could you provide us with more detail? What's a "line of force", and what's "reving"?

I don't think it's true. For electric fields, lines of force originate with positive charges and end at negative charges, unless they begin or end at infinity when the net charge of the system is non-zero. You could pick a location near the charges, where a test charge would experience a very strong force, and you could pick locations far away from charges, where the force would be weak, possibly even zero if everything's balanced just right. The field lines are perpendicular to surfaces of constant field strengths in 3D, and curves in 2D, so if you have a lone positive charge, the field lines would radiate straight out to infinity, and the surfaces of constant field energy (the equipotential surfaces) would be spheres around the charge.

You could pick a location near the charges, where a test charge would experience a very strong force, and you could pick locations far away from charges, where the force would be weak, possibly even zero if everything's balanced just right.
But that can also be because of the geometry losses right?...the lines of forces spread out so if the test charge is far away and so less lines of forces will fall on another charge (cause the lines of forces spread out with distance but actually depends on the geometry of the source charge) reducing the force.

So even if we consider this fact as true, the same thing will happen.

In fact, if this fact is true the inverse square relation of intensity with distance (for point charges) will be cause of the fact that the lines spread out with the distance travelled rather than the force by each line of force decreasing with the distance.

The field lines are perpendicular to surfaces of constant field strengths in 3D, and curves in 2D
:surprised

I'm sorta not getting what you mean by this...if I got it right, this is itself against the properties of lines of forces.

Matterwave
Gold Member
Force lines, or field lines are visual representations of the forces, and fields. They are not mathematically rigorous (the forms of the fields you can derive are, but they just tell you what it looks like).

In general, the denser the lines the more force there is, but of course there are an infinite number of lines, you just choose to draw a representative number. I wouldn't worry about field lines too much in terms of "strength", they are much more useful in telling you the direction of the force.

jtbell
Mentor
The field lines are perpendicular to surfaces of constant field strengths in 3D, and curves in 2D,
No, field lines are perpendicular to lines/surfaces of constant electric potential (equipotentials). The field is not generally constant on these lines/surfaces.

No, field lines are perpendicular to lines/surfaces of constant electric potential (equipotentials). The field is not generally constant on these lines/surfaces.
Thank you, I stand corrected.

Field lines are each equally strong.

To indicate the field is more or less strong, you add more or fewer lines.