The ``ideal'' answers may not be really ideal. In fact, there is often no unique answers.
But if students wonder, why their answer didn't get full marks, comparison to the ``ideal'' answers might help them to see why.
Labs
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Material 1 in hand | Material 2 in holder | Observed effect | Theoretical expectation
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rubber rubber repulsion repulsion
plastic plastic repulsion repulsion
metal metal repulsion/nothing repulsion
rubbed by wool rubbed by wool
metal metal repulsion/nothing repulsion
rubbed by styro. rubbed by styro.
rubber plastic attraction attraction
plastic rubber attraction attraction
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The metal-metal setups should show repulsion, but for whatever reason this effect is not
often definitely observed. The metal may simply lose its charge too quickly.
Hypothetical Law: There are two kinds of electric charge which we can tentatively label positive and negative. A charge has a quantitative value, the amount of the charge. Positive charge has positive value and negative charge has a negative value. The effect of a charge corresponds to the amount of charge summing the positive and negative contributions. Each kind of charge is separately conserved. It can neither be created or destroyed. An object becomes charged when it has a net amount of charge.
Discussion: The above law is actually incorrect in one respect. The two kinds of charge are NOT conserved separately, only there net sum is conserved. For example, an electron and a positron (the electron anti-particle) can mutually annihilate to to leave no charged particles. Pairs of equal and oppositely charged particles can be created too. These pair creation and annihilation events go on all the time, but in most terrestrial contexts at such a low level that a separate conservation of positively and negatively charged particles is a good approximation.
Discussion: What actually happens is that electrons from the cloth are transferred to the rod leaving the cloth with a net positive charge and the rod with a net negative charge.
In solids, electrons are overwhelmingly the most mobile charge carriers, and so they are almost always what is actually being transfered.
The process of charging by contact is triboelectrification. It's very common: it goes on all the time. But it's actually a very complex effect and predicting quantitatively what will happen from theory is not easy.
You may wonder since positive and negative charge attract how is a transfer possible at all that results in a charge separation.
Well it's not just the amount of charge that matters, but the arrangement that matters in attraction. For example, say one has 3 particles. One is positive with charge q and two are negative with each with charge -q. The three particles can be bound together. The positive one sits between the two negative ones and binds them to itself despite the repulsion between the negative particles. Actual bound charge systems require more explication, but they do exist like hydrogen anion (H-). Metals are another example. They can become highly charged positively or negatively, but they are still perfectly stable and just don't fall apart. The arrangement of charge is keeps them stable despite large imbalances.
A longer version is ``For every force of one system on a second system, there is force of the second system on first that is equal in magnitude and opposite in direction.''
In the experiment there was an attractive force of the charged rod in hand on the uncharged rod in the hanger. You could see this because the uncharged rod moved toward the charged rod. By the 3rd law, there should an attractive force of the uncharged rod on the charged rod. If your hand was sensitive enough, you would have felt the attraction of the charged rod to the uncharged rod. But your hand isn't sensitive enough. Interchanging the location of the rods, you observe easily the attraction of the charged rod to the uncharged rod.
Discussion: The 3rd law is actually not always obeyed even in classical physics. These violations don't come up much though. They all involve the magnetic force as far as I know.
The situation isn't so scandalous because a generalization of the 3rd law is obeyed.
Discussion: As mentioned above, the two kinds of charge are not, in fact, separately conserved although for many applications that is a good approximation. Net charge is conserved.
In fact, the net positive charge is distributed on the surface of the conductor. In electrostatic conditions, net electric charge can only be on the surface of conductor---a fact which requires a theoretical proof too long to give here, but not too long for your course. The actual distribution on the plate is probably a bit complex. Most charge is probably near the rod with little charge near the edges or the bottom side of the plate. The positive charge is attracted to the rod, but is self-repelled. It would take a very elaborate calculation or measurement to know the exact distribution of positive charge.
The positive charge creates an electric field that probably mostly points away from the plate at least far from the edges. Above the plate, it points up. Below the plate, it points down.
Above the plate, the positive charge field adds to the upward rod field to give a stronger electric field.
Below the plate, the positive charge field tends to cancel the upward pointing rod electric field. Experimentally, the cancellation looks pretty complete.
The overall effect of the metal plate is called electrical shielding. Because charge can flow in metal, the charge tends to flow so as to cancel an applied field in certain regions around the conductor.
Electrical shielding is pretty common both by design and accident. Nearly complete shielding in a region is achieved by enclosing the region entirely in metal. The enclosure is called a Faraday cage.
The results are consistent.
Since rubber acquires a negative static charge from contact with woool, wool should acquire a positive charge.
Since plastic acquires a positive static charge from contact with styrofoam, styrofoam should acquire a negative charge.
For hand-drawn graphs, the scale of the axes should try to satisfy two criteria:
In this case, the theoretical expectation is that the E-field should fall off as the inverse-square of distance.
You should see if this is roughly true. If distances double, do E-fields decrease by 4? If they don't maybe you should re-do your measurements.
kq
E = ----- ,
r**2
where k = 8.98755*10**9 = approximately 10**10 in MKS units is Coulomb's constant,
q is the charge on the graphite ball,
and r is the distance from the ball center to the field mill sensor.
We can linearize this formula by setting x=1/r**2.
This gives
E=kqx ,
where E is the dependent variable,
x is the independent variable,
kq is the slope,
and the y-intercept is zero.
We plot E on the vertical scale and x=1/r**2 on the horizontal scale.
With an AC field of frequency f, the electric field direction switches direction by 180 degrees at
frequency 2f.
In this case the potential across Delta s also switches sign at a frequency of 2f.
A multimeter reading AC potential gives NOT the instantaneous potential which alternates to quickly
for a human to read in most cases and NOT the mean potential which is zero, BUT the
root mean square (RMS) potential: sqrt(
So in for an AC field, one gets the RMS electric field component E_com=Delta V/Delta s.
There is no minus sign since RMS quantities are always positive.
In the rest of this laboratory, when we say electric field, electric field component, and
potential, we usually mean the RMS electric field, electric field component, and potential.
For this experiment where we use an AC power source and create an AC field,
one has to choose a reference direction for the electric field.
Choose one metal plate to be positive and one to be negative.
Now the electric field lines (E-field lines) run from the positive to negative plate by convention.
In actual, fact their direction changes at frequency 2f.
Explain why the test leads give the biggest reading when one is aligned with the
E-field lines and why the meter reading is proportional to the (RMS) electric field magnitude for
that biggest reading.
In the
When the test leads are aligned with the electric field, the electric field magnitude = E_com = Delta V/Delta s.
Since Delta s is held constant thoughout the experiment, Delta V for Delta s aligned with the field is proportional
to the electric field magnitude with 1/Delta s being the proportionality constant.
Answer: The electric field has its largest component in the direction of the electric field since then
the electric field magnitude and its component are equal.
In all other directions, the component is less: a vector component is always less than or equal
to a vector magnitude.
In the direction perpendicular to the electric field, the component is zero.