Download Equipotential Lines and the Electric Dipole 1 Purpose 2 Theory

Equipotential Lines and the Electric Dipole
1
Purpose
The equipotential lines of an electric dipole will be mapped. This map will then be used to
generate electric field lines and investigate the concepts of electric potentials.
2
Theory
A semiconductive paper is used to map the equipotential lines of an electric dipole. The
electric field lines are then generated using the equipotential lines. Small disk conductors
are used to simulate point charges.
An equipotential line (2-D) or equipotential surface (3-D) is a line or surface which
consists of points that are at the same potential (Vba = 0), or at a constant potential
difference from a given point not on the equipotential line (Vba = constant). No work is
required to move a charge from one point to another on an equipotential line, and according
to the definition of work
∫
⃗
⃗ · dr
W = qE
this can only be satisfied if the electric field is ALWAYS perpendicular to the equipotential
lines. Thus by mapping out the equipotential lines one can generate the electric field lines.
For the 3-D electric field around a point charge, the electric potential is given as
V =−
∫
Edr = −
q ∫ dr
4πϵo r2
q
4πϵo r
The principle of superposition is used to calculate the net electric potential due to group
of point charges,
n
n
∑
qi
1 ∑
V =
Vi =
4πϵo i=1 ri
i=1
V3D =
The electric potential of a dipole is given as:
V =
q (r− − r+ )
q d cos θ
≈
4πϵ0 r− r+
4πϵ0 r2
1
(far away)
3
Procedure
1. Set the voltage (potential difference) between the two conductors (dipole configuration)
at 20 V. Connect the negative probe of the multimeter to the negative conductor and
using the positive probe obtain the voltage such to find equipotential points.
2. Draw in 7 equipotential lines (Vba = 2V, 4V, 7V, 10V, 13V, 16V, 18V ) for a dipole configuration with large dipole moment p = qd (charge is widely spaced approximately 6
cm).
3. Obtain the voltage along the longitudinal and transverse axis of the dipole with small
dipole moment p (charge is closely spaced aproximately 3 cm) at 1 cm interval.
4. Obtain the voltage along a concentric circle centered on the small p dipole at 10◦
interval.
4
Interpretation of Results
1. Draw in the electric field lines of the large dipole moment dipole configuration.
2. Does your electric field pattern resemble the point charge dipole pattern given in your
physics textbook? How are the patterns similar? How are they NOT similar?
3. Subtract 10V from your obtained voltages in procedure 3 to simulate a positive and
negative charge giving positive and negative potentials. Plot your ’corrected’ voltage
versus distance r for the longitudinal and transverse axis of the small p dipole. Discuss
q r− −r+
your plot(s) in terms of the theoretical result V = 4πϵ
.
0 r− r+
4. Subtract 10V from your obtained voltages in procedure 4 to simulate a positive and
negative charge giving positive and negative potentials. Plot the ’corrected’ voltage
versus cos θ of the small p dipole along the concentric circle. Measure your angles
with respect to the positive longitudinal axis, that is, the 0◦ is on the longitudinal
axis that has the positive charge. Discuss your plot in terms of the theoretical result
q d cos θ
.
V ≈ 4πϵ
r2
0
2