Download Lab 2 Equipotential Lines

Lab 2 Equipotential Lines
Introduction
In this lab, we will measure the equipotential lines generated by a voltage source on a conductive
surface. We will also relate the potential lines to the electric field.
Equipment
Power supply, DMM, resistive paper and probes.
Background
Electrical equipotential lines are completely analogous to gravitational equipotential lines. A mass
will always have the same gravitational potential energy at the same height. The height is
described exactly by a topographical map. Each line on the topographical maps corresponds to a
specific amount of potential energy.
sparse contour lines
means a smaller slope
200 ft rise over 2,000 ft run
dense contour lines
means a larger slope
200 ft rise over 200 ft run
Batteries provide electrical potential energy to charges just like the Earth provides gravitational
potential energy to masses. To measure the gravitational potential, we use altitude. To measure
the electrical potential, we use voltage. The higher the altitude of a mass, the more gravitational
potential energy it has. The higher the voltage of a charge, the more electrical potential energy it
has.
In the case of gravity, the closer the altitude lines are to each other, the steeper the terrain and the
harder gravity pulls down on an object. This results in a larger gravitational field. In the case of
electricity, the closer the electric potential lines are to each other, the harder the push from the
electric force and the larger the electric field.
page 1
Below left is shown the electrical potential function for a positive point charge placed at the origin.
Think of it as a volcano. Equipotential lines are rings that indicate the “altitude”. The electric fields
reflect the slope around the rings. The steeper the slope, the longer the electric field vector. Also,
they point “downhill” or where a positive charge would slide when released.
V=2
V=1
V=0.5
Experiment: Setup
The terminals of a power supply tries to change the potential of the
location they touch to the same potential as the terminal. If the thing
that is touching the terminal is metallic, the potential spreads
unchanged. Otherwise, it spread out with a decreasing potential.
This is what resistance does to the voltage.
+DMM (V) –
The terminals will be connected to two locations on a piece of
resistive paper. Use the resistive paper with two dots on it. Connect
the two dots of the resistive paper as in the diagram on the right.
Make sure a good contact is made between the metal contacts and
the paper. Mark the size and locations of the two metal contacts on
the graph paper. Use the grid of the conductive paper as a guide.
Check the connections by making sure that the voltage at the “+” end
is 20 V and the voltage at the “–“ end is 0 V.
Connect the “COM” side of the DMM to the “–” side of the power
supply and connect the “V” side of the DMM to the red probe wire.
Use only the red probe here.
20 V
+
power
supply
–
0V
Mapping Equipotential Lines
Find 10 points on the resistive paper where the voltage is 10 V. Space them out such that they go
across the page or around the dots. Plot the points on the graph paper at the end of this file.
Repeat for 12 V, 14 V, 16 V, 8 V, 6 V and 4 V for a total of 7 equipotential lines.
This is the pattern of equipotential lines for a dipole which consists of two points, one where the
electric potential is high and another where the electric potential is low.
page 2
Mapping the Center Line
Along the line connecting the two dots, use the probe to measure the voltage at every square.
Skip over the dots and leave them blank.
Graph the voltage as a function of the position along the axis. Connect the adjacent points with a
straight line and calculate the slopes of the potential function between them. Skip over the two
dots.
The electric field relates to the electric potential this way. It is the negative of the slope of the
potential function. Sketch the electric field vectors between these points taking into account the
magnitudes. Use a scale such that a 1 cm long vector represents 100 V/m.
E =−
ΔV
Δr
Questions
1. If a positive test charge were place on this line between the terminals, in which direction will it
move spontaneously?
2. If a positive test charge were place on the line segment left of the terminal on the left, in which
direction will it move spontaneously?
3. If a positive test charge were place on the line segment right of the terminal on the right, in
which direction will it move spontaneously?
4. In general, a positive test charge moves in which direction when it is immersed in an electric
potential?
page 3
page 4