9478 / 2027
Electromagnetic Forces overview

Topic 2 of 9

Magnetic sources and field patterns

Permanent magnets and electric currents produce magnetic fields. A field pattern describes direction at each point; it is separate from the force or path of a particular object placed there.

A compass's north-seeking end indicates the local magnetic field direction. Outside a bar magnet, field lines run from north to south, returning inside it to form closed paths. Lines do not cross. Closer spacing can represent greater field strength within a consistently drawn pattern, but the lines are not material tracks.

The presence of a field does not mean every object experiences a nonzero force. For example, magnetic force on a charge depends on its velocity as well as the field. Keep the source of the field distinct from the body whose force is being considered.

Read the viewpoint and current direction

A dot means a named direction out of the page towards you, like an approaching arrowhead. A cross means into the page away from you, like the tail of an arrow. Check whether the symbol labels current, field or force. For an ordinary page view, use x right, y up and z out of the page; a separate end view must say where the observer is looking from.

Straight wire: look along its axis

Straight wire: look along its axisA brown central dot denotes conventional current out of the page. Three concentric teal circles have anticlockwise field arrows. At the point immediately to the right of the wire the field is upward, tangent to a circle. These are magnetic field lines, not particle paths.I outAt the right: B points up.

Brown dot: current towards you. Teal circular arrows: magnetic field anticlockwise. Reversing the current reverses the field.

Flat coil: view from the right along its axis

Flat coil: view from the right along its axisThe observer is on the right of the axial-section view, looking left towards the flat coil. Conventional current is anticlockwise in this face view, shown by brown arrows around the winding. The teal central dot denotes magnetic field towards this observer, which is rightward in the axial section. The circular brown path is the winding, not a circular magnetic-field line around the coil centre.B towards youCurrent anticlockwiseView from the right

Here the central dot means field towards you, not wire current. The observer stands on the right of the next axial-section view.

Flat coil: a section through its axis

Flat coil: a section through its axisThis axial section cuts the winding at top and bottom. Brown dot at the top means current out of the page; brown cross at the bottom means current in. Two closed noncrossing qualitative field paths point right through the interior and return left outside the coil. The central field arrow points right along the horizontal coil axis. The coil face in the preceding view was observed from the right.I outI inInterior B is rightward.Observer for face view is on the right.

The current symbols are wire cross-sections. Field lines pass through the interior along the axis and return outside; their shapes here are qualitative.

Long solenoid: an axial section

Long solenoid: an axial sectionRepresentative upper wire cuts carry current out of the page, and lower cuts carry current in. They belong to turns whose unseen parts connect outside the section; the drawing does not count the actual turns. Two noncrossing closed field paths run right through the interior, return left outside and bend at the ends. The left end is south and right end north. Approximately parallel central lines describe the interior away from the ends, not uniform field everywhere.SNRepresentative wire cutsNot a count of the actual turns

Top current out, bottom current in gives B right inside: S at the left, N at the right. The central region is approximately uniform; the ends and outside are not.

The straight-wire view and the flat-coil face view use their own stated viewing directions. In the matching coil and solenoid axial sections, top-wire current is out of the page and bottom-wire current into it, giving an interior field to the right. Return lines close the pattern outside.

Long straight wire

Field lines are concentric circles in planes perpendicular to the wire. Point your right thumb along conventional current; your curled fingers give the field direction. Current out of the page produces anticlockwise field lines in that face-on view. Immediately to the wire's right, the tangent field direction is upward.

Reversing current reverses every field direction. The lines are circular, not radial outward from the wire. A compass lies tangent to a local circle, not along the wire's current.

Flat circular coil

The field passes through the coil's centre along its axis and returns outside the coil. Viewed at a face, anticlockwise current gives a central field towards the observer; clockwise current gives it away. Curl the right-hand fingers with current around the coil and use the thumb for the central axial field.

The face and axial-section drawings describe the same arrangement from different directions. Do not draw the whole coil's field as concentric circles in the coil's plane: that is not the field pattern through its centre.

Long solenoid

A solenoid is a coil with many turns along a length. Well inside a long solenoid and away from its ends, the field is approximately uniform, with parallel, similarly spaced lines. Outside it, weaker field lines return from the north end towards the south end. The end region spreads out, so interior uniformity does not extend unchanged through the ends.

Curl the right fingers with current around the turns. The thumb gives the interior field and points towards the solenoid's north end. In the shown axial section, the interior field is right and the right end is north. Reversing current swaps the effective poles.

Map a field and distinguish its strength from flux

Move a small compass to several positions, record its north-end direction and connect smooth tangents. Keep current, source geometry and nearby magnetic objects fixed. Repeat with reversed current to compare the source contribution with Earth's or other background fields. Iron filings can suggest the pattern but do not by themselves identify its direction.

Magnetic flux density B describes the local field and is measured in teslas, T. Magnetic flux Φ describes the field through an area and is measured in webers, Wb. For this supplied uniform-field model with the area perpendicular to B, use Φ = BA.

A rough field of 0.1 T through an area of order 10-3 m2 suggests flux of order 10-4 Wb. More precisely, a 0.0800 T perpendicular field through a 2.00 cm by 3.00 cm rectangle gives:

A = (0.0200)(0.0300) = 6.00 × 10-4 m2
Φ = BA = (0.0800)(6.00 × 10-4)
= 4.80 × 10-5 Wb = 48.0 µWb

Doubling this area at unchanged B doubles the flux, while local B stays the same. One microweber is 10-6 Wb. Using the force definition of the tesla, and J = N m and C = A s:

1 Wb = 1 T m2 = 1 N m/A
= 1 J/A = 1 V s
= 1 kg m2 s-2 A-1

Keep the quantity and unit together: B in T and Φ in Wb are different, even when one uniform field is used to calculate both.

Optional check A long straight wire carries conventional current out of the page towards you. What is the direction of its magnetic field immediately to the right of the wire?
A long straight wire carries conventional current out of the page towards you. What is the direction of its magnetic field immediately to the right of the wire?