Physics 261
Electric Field Mapping
An electric field is a vector field, having both magnitude and direction. It’s magnitude is proportional to the force felt by a unit positive charge, and its direction is the direction of this force. Motion
of a charged object in or opposite the direction of the field results in a transformation of energy.
Motion in the direction of field results in increased kinetic energy and decreased potential energy.
Motion against the field requires work to be done, and results in increased potential energy. In the
case of static electric fields, potential energy is sometimes simply referred to as “the potential.”
No work is done, and no energy transformation occurs, when the motion is perpendicular to the
field. Such paths, perpendicular to the field direction, are called equipotential lines. As it happens,
such equipotentials are easier to measure than electric fields directly. Mapping out equipotentials,
and remembering that field lines are perpendicular to them, allows one to then map out the field.
That’s what you’ll be doing on several different electrode arrangements (see Figure 1).
Figure 1: Electrode geometries.
Each arrangement is painted on graphite-impregnated plates with silver paint, a conductor that
acts as an electrode. A plate is secured to the bottom of a field mapping board (see Figure 2) that
is wired into the circuit shown. The power supply should be set to between 2 and 6 volts.
Equipotential lines are probed with a ”wand” (see Figure 3) and marked on a piece of paper
secured (so as to be immobile) to the top of the board. A hole located immediately above a contact
on the lower arm of the probe (check to see that this is in fact the case) allows points to be marked
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Figure 2: Schematic diagram of equipotential mapping setup.
with a pencil. Note that the wand is not configured properly because adjustment screws have been
loosened or the wand has been distorted by mistreatment. Readjust as necessary to align things
and ensure that the contact point touches the graphite plate. Find and mark a series of positions
with the same voltage reading sufficient to sketch, with dotted lines, a closed loop (why must the
equipotential be a closed loop?). Continue in this way until you have located 5-6 equipotential lines.
Before removing the paper from the mapping board, draw the electrode configuration on it by
tracing with a template fit over locating pins on the board. Be sure to used a template that matches
the graphite plate configuration and to orient it to match the plate orientation. Repeat this process
for all five configurations.
With the equipotential maps, draw in electric field lines (indicated with solid lines and arrows to
indicate direction) by crossing the equipotential lines perpendicularly. Near electrodes, the equipotential lines should be roughly parallel to the edges, so the field lines should be roughly perpendicular
to these edges (why?). The density of field lines should be approximately constant in any given region of the map, and show, by this density, where the field is strongest (densely packed lines) and
weakest (sparsely populated with lines). Be prepared to explain your maps.
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Figure 3: Using the wand to map out the equipotential lines.
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