Field line

Field line (or power line) is a term in physics. Field lines are imaginary or drawn lines (generally curved), which illustrate the force exerted by a field on a test body. The down to a field line tangent is the direction of force on the respective point of contact; the density of the lines indicates the thickness of the field.

Examples

• Gravitational field lines illustrate the gravity on a sample mass. Earth - the Earth's gravity - these field lines are practically straight lines perpendicular lines or vertical, you can make it visible by a plumb line.
• Electric field lines illustrate the Coulomb force on electric test charges. You begin to positive charges and end on negative charges (or at infinity, respectively ).
• Magnetic field lines illustrate the magnetic forces on the magnetic poles. They are self-contained, occur at the north pole of a magnet from this and from the South Pole in him. In general, they always point in the direction in which shows the north pole of a freely rotating compass needle. Magnetic dipoles (eg compass needles ) align themselves along the field lines, as the experiences a pole a force in the field direction and the other pole a force in the opposite direction.

The shape and density of magnetic and electric field lines can be made using simple demonstration experiments make it visible: iron - like all ferromagnetic materials - magnetized by a magnetic field. Therefore, store iron filings, for example, on a sheet of paper to each other and form chains along the magnetic field lines. Similarly, the electric field acts on semolina grains in a viscous dielectric liquid such as castor oil. The grains are electrically polarized by the field and thus arrange themselves along the electric field lines.

Properties

• The amount of the field strength is proportional to the field line density, and not in the two-dimensional representation, but in the area with the number of field lines that pass through a field lines oriented orthogonal to the unit area.
• Field lines never intersect each other. If overlap multiple fields in a point, enter the field lines in the direction of the resultant force.
• Field lines of source fields (such fields of electrical charges, or gravitational fields ) go from one point or end in a point.
• Field lines of eddy fields (such as magnetic fields or electric fields that are induced by changing magnetic fields) have no beginning and no end, but are closed lines.
• The course of the lines can be clearly explained by the following mnemonic: field lines "will" always be as short as possible, but repel each other.
• If the field lines are straight and parallel in a given area and have a constant density, it is called a homogeneous field. This is not the case, ie inhomogeneous field.
• If history and density of the lines in the course of time does not change, it is called stationary field.

Direction (orientation) of field lines

The field lines point in the direction of the field strength:

• The magnetic field to show the field lines in the direction in which displays the north pole of an elementary magnet ( miniature compass). In the vicinity of a permanent magnet, the field lines thus run from the North to the South Pole.
• The electric field show the field lines in the direction of the force acting on a positive test charge. Thus, in an electrostatic ( emanating from charges ) box to extend from the positive to negative charge.

Justification of the field representation by means of lines

Using the example of a charged sphere, which exerts a force on other charged particles in the environment, different ways of an illustrative graphical representation of the field can be discussed.

• In the left image the weakening field is represented by lower color saturation. This has the great advantage that questions such as " Is there a force between the lines of force? " Not even asked because the surface is completely covered. The disadvantage of this representation is that it is not easy to picture the direction of the force - can be seen - this is the direction of the strongest change of color saturation. Deeper questions about whether the field is radially symmetric ( as in the middle picture ) or, for example, designed with left-hand twist as in the right picture, you can not answer with the color saturation representation.
• These subtleties can be represented easily in the field line images, but with the disadvantage that often questions are asked such as " Are there only these field lines or are more of them in between? " Or " Is there further out more places without field lines? " Or "Tracks a charged particle on a tangential path and alternately much less force, when it crosses the lines of? "
• The question of whether a charged sphere, the mean or, for example, applies the right representation can only be experimentally or through knowledge of special "rules" (field lines terminate on conductive surfaces always perpendicular ) answer (Correct is the center figure ). In the left illustration, this question is not even posed.
• How can you graphically represent whether a particle is attracted or repelled by the charged sphere? The chroma display this is not possible. The other two representations allow discrimination by arrowheads on the lines.
• The line representation offers certain advantages related to the graphical solution of differential equations ( direction field ).
• The line representation is easier to draw and printing techniques to reproduce. Historically this is certainly the main reason why it has prevailed.

Theoretical background

A field line indicates a path along a vector field on a differentiable manifold, for example, along the electric field in the spatial domain. Since the vector field each point of the manifold assigns a tangent vector, field lines but in order to speak meaningfully of " field line density " can, must have each other distances, it becomes clear why the concept of " field line " is used only for qualitative illustration.

Typical vector fields, as they are the subject of electrodynamics, can be disassembled with the decomposition theorem in a gradient and a vortex field component. The field lines of the gradient field extending between the sinks and the sources, the eddy field, all field lines are closed loops that do not intersect.

Formally, characterized, for example, in the electric field, the field lines at the point by the equation

Said infinitesimal continuation of which passes through the point line represents field. Satisfy this equation due to the definition of the cross product, all vectors which are parallel to the lines at that point. In the two-dimensional case (), this equation reduces to

The field pattern allows an informal access to the Gaussian integral theorem: all field lines of the field, which have their origin in an area that is bounded by the edge, must end either in this area or discharged through the border pass. Consequently, the following applies:

In words: The total source strength of the vector field in a region is equal to the flux through its boundary surface. It follows immediately for spherically symmetric problems

Since the field lines on the sphere with radius " distribute ". This proportionality can be found eg in the law of gravitation or Coulomb's law.