We recommend using aĪuthors: Paul Peter Urone, Roger Hinrichs Use the information below to generate a citation. Then you must include on every digital page view the following attribution: The electric field lines have the electric field vector as a tangent and their density is proportional with the magnitude of the electric field. In our 2D case we have two kinds of lines, the electric field lines and the equipotentials. If you are redistributing all or part of this book in a digital format, Field lines are an useful tool for visualizing vector fields. Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the If magnetic monopoles existed, then magnetic field lines would begin and end on them. It is a distinct difference from electric field lines, which begin and end on the positive and negative charges. The last property is related to the fact that the north and south poles cannot be separated. They go from the north pole to the south pole. Magnetic field lines are continuous, forming closed loops without beginning or end. Electric field lines are drawn lines that follow the path of the electric field, originating from a positive charge (or charged object) and terminating at a.You can add or remove charges and vary the magnitude of each charge. Magnetic field lines can never cross, meaning that the field is unique at any point in space. This Demonstration shows the electric field lines and associated contours of the electric potential due to a collection of movable point charges.It is exactly proportional to the number of lines per unit area perpendicular to the lines (called the areal density). The strength of the field is proportional to the closeness of the lines.A small compass will point in the direction of the field line. The direction of the magnetic field is tangent to the field line at any point in space.The properties of magnetic field lines can be summarized by these rules: We use magnetic field lines to represent the field (the lines are a pictorial tool, not a physical entity in and of themselves). Gravitational fields map gravitational forces, electric fields map electrical forces, and magnetic fields map magnetic forces.Įxtensive exploration of magnetic fields has revealed a number of hard-and-fast rules. The field represents the object generating it. Note the symbols used for field into and out of the paper.Ī field is a way of mapping forces surrounding any object that can act on another object at a distance without apparent physical connection. A small compass placed in these fields will align itself parallel to the field line at its location, with its north pole pointing in the direction of B. In both cases, the fields represent only the object creating them and not the probe testing them.) Figure 22.16 shows how the magnetic field appears for a current loop and a long straight wire, as could be explored with small compasses. (This is analogous to the way we tested electric fields with a small test charge. If two lines did cross, then the force on a charge would have two. Small compasses used to test a magnetic field will not disturb it. Field lines point in the direction of the electric field E. (c) If the interior of the magnet could be probed, the field lines would be found to form continuous closed loops. The strength of the field is proportional to the closeness (or density) of the lines. (Recall that the Earth’s north magnetic pole is really a south pole in terms of definitions of poles on a bar magnet.) (b) Connecting the arrows gives continuous magnetic field lines. (a) If small compasses are used to map the magnetic field around a bar magnet, they will point in the directions shown: away from the north pole of the magnet, toward the south pole of the magnet. So, for your particle to be advected exactly along the field lines, you have to demand that its equation of motion is not the Newton one, namely go in the limit of zero inertia (and no radiation).Figure 22.15 Magnetic field lines are defined to have the direction that a small compass points when placed at a location.
The simple fact that the particle has "inertia" makes it drift from the path along the field lines. Without considering the back reaction of EM emission from the particle itself and relativistic effects. In Cartesian coordinates on a 2D plane, let $$\mathbf(t))