Physics Online
Electric Dipole
Charged objects create a vector property in their surroundings called an electric field. The
magnitude of the electric field of a point charge can be calculated as follows:
E = kq/r2
k = 8.99E9 Nm2/C2
q = magnitude of charge
r = distance between charge and point in space
If an object is electrically neutral as a whole, but has equal and opposite charges separated by
a known distance, then the object is called an electric dipole. Many molecules can be treated as
electric dipoles for the purpose of calculating their electric fields. We can calculate the
electric field, E, at a distance z from the center of the dipole at a point on its axis. The dipole
has charge separation d and charges +q and –q. Using vector addition and the above formula
for electric field of a point charge, we can derive an expression for the net electric field along
the axis connecting the two charges:
E = E(+) – E(-)
E = kq/r+2 – kq/r-2
E = kq/(z – d/2)2 – kq/(z + d/2)2
E = kq[(z – d/2)-2 – (z + d/2)-2]
E = kq/z2[(1 – d/(2z))-2 – (1 + d/(2z))-2]
If we assume that z >> d, then we can use just the first two terms of the
binomial expansion as follows:
(1 – d/(2z))-2 = 1 + d/z
(1 + d/(2z))-2 = 1 – d/z
Substitution of the approximations into the formula for the electric fields
yields the following:
E = kq/z2[(1 + d/z) – (1 – d/z)]
E = kq/z2[2d/z]
E = 2kqd/z3
We can use the definition of the electric dipole moment, p, to further simplify
the above equation.
p = qd
E = 2kp/z3
If we place an object with charge q0 in the presence of this electric field, then
we can calculate the magnitude of the electric force on the charged particle.
Fe = qoE
Fe = 2kpq0/z3
By Newton’s third law, this will also be the magnitude of the force on the dipole. If this is
the only horizontal force, then Newton’s second law can be used to relate the horizontal
force on the dipole to the acceleration of the dipole.
ΣFx = max
[1] 2kpq0/z3 = max
In this experiment, we will use water molecules as the dipoles and a balloon as the charged
object. A water molecule has the following properties:
p = 6.2E-30 C*m
m = 2.992E-26 kg
We can use two-dimensional kinematics to approximate the acceleration of the water
molecules in the presence of the charged balloon. Then we can calculate the magnitude of
the charge on the balloon.
If we assume that the acceleration is uniform (perhaps not a wise assumption, but this will
greatly simplify our analysis) and that the acceleration in the y direction is only due to gravity
(another questionable assumption), then the kinematics equations are the following:
[2] Δy = ½gt2 (using down as positive)
[3] Δx = ½axt2
Physics is fun!
Equipment You Procure
 faucet and sink
 metric tape measure
 human hair, hairless human skin, glass,
paper, and a furry animal (optional)
 digital camera
z
Δy
Equipment from Kits
 digital calipers
 balloon
Δx
Procedures
Derivations
1) Solve equation [2] symbolically for t2 and substitute your symbolic solution into
equation [3].
2) Solve equation [3] symbolically for ax and substitute your symbolic solution into
equation [1].
3) Solve equation [1] symbolically for q0, the charge of the balloon. There should be
only one division symbol and one 2 (or 0.5).
Experiment
1) Measure the distance from the faucet to the bottom of the sink, Δy.
2) Slowly open the faucet so that drops come out (the above photo is not accurate in
this respect). Observe the location where the water hits the bottom of the sink. If
you use a stream instead of drops, you may have your report returned for
resubmission.
3) Rub the balloon on your head for several seconds to negatively charge the balloon. If
you don’t have enough hair on your head, then rub the balloon on your chest hair or
a puppy. Record the material. Record the number of rubs or time of rubbing.
4) Place the balloon halfway between the end of the faucet and the bottom of the sink
and a small horizontal distance away from the drops. The part of the balloon that
you rubbed should be facing the drops. Measure the approximate distance from the
balloon to the drops, z. Note that the picture uses a stream to make it easier to see.
You will use drops.
5) Measure the distance that the drops of water deflect, Δx.
Calculations
1) Use your theoretical equation to calculate q0, the magnitude of the charge of the
balloon.
2) Calculate the number of excess electrons on the balloon, given that e = 1.60E-19 C.
3) Calculate the additional mass acquired by the balloon from the electrons, given that
me = 9.11E-31 kg.
Repeat this experiment several times with a different pair of substances, different amount of
rubbing or different distances. Try to keep the contact area during rubbing roughly
consistent. Perform a sufficient number and variety of experiments to test the
following claims:
1) The distance (z) will not affect the calculation of charge (conservation of charge),
other things held constant.
2) The greater the amount of rubbing, the greater the charge, other things held
constant.
3) The greater the distance between two substances in the triboelectric series, the
greater the charge (see http://en.wikipedia.org/wiki/Triboelectric_series), other
things held constant.
The two men in the front row and the man in the middle of the back row appear to have
hairless chests. The triboelectric effect would therefore be different than that of the hairy
chests of the men in the back left and back right.
The above animal’s triboelectric effect can be compared to that of human hair.