Field lines are drawn so that their direction gives the direction of the field and their spacing shows its strength. Electric flux, Φ = EA cos θ, measures how much field passes through a surface.
The electric field has a value and a direction at every point, but it cannot be seen. Michael Faraday introduced a way to draw it: electric field lines.
A field line is a curve drawn so that the tangent to it at each point is in the direction of the field at that point. A positive test charge released at rest starts to move along the field line through its position.
Field lines are a drawing method, not physical objects. The field exists at every point, including the points between the lines that are drawn. The number of lines in a picture is a choice made by whoever draws it.
Why can two electric field lines never cross?
At every point, the field has one value and one direction. A field line’s direction at a point is the field’s direction there.
If two lines crossed at a point, there would be two different directions for the field at that one point. A test charge placed there would experience one force in one direction, so this cannot happen.
At a point where the field is zero, such as the midpoint between two equal charges of the same sign, there is no direction at all, and no field line passes through it.
Electric flux, Φ, measures how much electric field passes through a surface. For a flat surface of area A in a uniform field E:
Φ = E A cos θ
Here θ is the angle between the field and the normal to the surface, the line perpendicular to it. The SI unit of flux is N m²/C.
In the field-line picture, flux is proportional to the number of lines passing through the surface.
Flux depends on angle. The same field and the same surface give the maximum flux when the surface faces the field, and zero flux when the surface is edge-on.
A flat loop in a uniform field is rotated from facing the field to edge-on. What happens to the flux through it?
The flux decreases from EA to 0.
Φ = EA cos θ, where θ is the angle between E and the normal to the loop. Facing the field, θ = 0° and Φ = EA. As the loop turns, θ increases and cos θ decreases. Edge-on, θ = 90° and Φ = 0.
In the field-line picture, the loop presents a smaller cross-section to the lines as it turns, so fewer pass through it.
1An electric field line is drawn so that…
2Field lines start and end…
3Where field lines are close together, the field is…
4Why do two field lines never cross?
5For a flat surface in a uniform field, the electric flux is…
6The flux through a flat loop is zero when the loop is…
Next: the electric dipole, a pair of equal and opposite charges.
Noescio