What Are the Magnetic Field Strength and Direction at Points a to C in the Figure Below?

Learning Objective

By the end of this section, you will be able to:

• Define magnetic field and describe the magnetic field lines of various magnetic fields.

Einstein is said to have been fascinated past a compass as a child, perhaps musing on how the needle felt a force without direct concrete contact. His power to think deeply and clearly almost action at a distance, particularly for gravitational, electric, and magnetic forces, later enabled him to create his revolutionary theory of relativity. Since magnetic forces act at a distance, we define a magnetic field to represent magnetic forces. The pictorial representation of magnetic field lines is very useful in visualizing the force and direction of the magnetic field. As shown in Figure 1, the management of magnetic field lines is defined to be the management in which the n cease of a compass needle points. The magnetic field is traditionally called the B-field.

Figure 1. Magnetic field lines are defined to take the direction that a small compass points when placed at a location. (a) If small-scale compasses are used to map the magnetic field around a bar magnet, they volition point in the directions shown: away from the north pole of the magnet, toward the southward pole of the magnet. (Recall that the Earth'south north magnetic pole is really a southward pole in terms of definitions of poles on a bar magnet.) (b) Connecting the arrows gives continuous magnetic field lines. The strength of the field is proportional to the closeness (or density) of the lines. (c) If the interior of the magnet could be probed, the field lines would be establish to form continuous closed loops.

Minor compasses used to test a magnetic field will not disturb it. (This is analogous to the fashion nosotros tested electrical fields with a small test charge. In both cases, the fields represent only the object creating them and not the probe testing them.) Effigy 2 shows how the magnetic field appears for a current loop and a long straight wire, as could be explored with minor compasses. A small compass placed in these fields volition align itself parallel to the field line at its location, with its due north pole pointing in the direction of B. Note the symbols used for field into and out of the paper.

Figure 2. Small compasses could exist used to map the fields shown here. (a) The magnetic field of a circular current loop is like to that of a bar magnet. (b) A long and straight wire creates a field with magnetic field lines forming circular loops. (c) When the wire is in the plane of the paper, the field is perpendicular to the newspaper. Notation that the symbols used for the field pointing inward (like the tail of an pointer) and the field pointing outward (like the tip of an arrow).

Making Connections: Concept of a Field

A field is a way of mapping forces surrounding any object that tin can deed on another object at a distance without apparent concrete connectedness. The field represents the object generating it. Gravitational fields map gravitational forces, electric fields map electrical forces, and magnetic fields map magnetic forces.

Extensive exploration of magnetic fields has revealed a number of difficult-and-fast rules. We use magnetic field lines to represent the field (the lines are a pictorial tool, not a concrete entity in and of themselves). The backdrop of magnetic field lines tin be summarized by these rules:

1. The direction of the magnetic field is tangent to the field line at any point in space. A small-scale compass volition indicate in the direction of the field line.
2. The forcefulness of the field is proportional to the closeness of the lines. It is exactly proportional to the number of lines per unit area perpendicular to the lines (called the areal density).
3. Magnetic field lines tin can never cross, meaning that the field is unique at any betoken in infinite.
4. Magnetic field lines are continuous, forming closed loops without beginning or end. They go from the north pole to the due south pole.

The last holding is related to the fact that the north and south poles cannot be separated. It is a distinct departure from electric field lines, which brainstorm and cease on the positive and negative charges. If magnetic monopoles existed, then magnetic field lines would begin and cease on them.

Section Summary

• Magnetic fields can be pictorially represented by magnetic field lines, the backdrop of which are as follows:
  • The field is tangent to the magnetic field line.
  • Field strength is proportional to the line density.
  • Field lines cannot cross.
  • Field lines are continuous loops.

Conceptual Questions

1. Explain why the magnetic field would non be unique (that is, not have a single value) at a indicate in space where magnetic field lines might cantankerous. (Consider the direction of the field at such a point.)
2. List the means in which magnetic field lines and electric field lines are like. For case, the field management is tangent to the line at any betoken in space. As well list the means in which they differ. For example, electric forcefulness is parallel to electric field lines, whereas magnetic force on moving charges is perpendicular to magnetic field lines.
3. Noting that the magnetic field lines of a bar magnet resemble the electric field lines of a pair of equal and opposite charges, exercise you expect the magnetic field to chop-chop decrease in strength with distance from the magnet? Is this consistent with your experience with magnets?
4. Is the Earth's magnetic field parallel to the basis at all locations? If not, where is information technology parallel to the surface? Is its force the same at all locations? If non, where is it greatest?

Glossary

magnetic field:

the representation of magnetic forces

B-field:

another term for magnetic field

magnetic field lines:

the pictorial representation of the strength and the direction of a magnetic field

direction of magnetic field lines:

the direction that the northward end of a compass needle points

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Source: https://courses.lumenlearning.com/physics/chapter/22-3-magnetic-fields-and-magnetic-field-lines/

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