Practice Test
(4 problems to attempt in a 50-minute time span). Suggested, not required.
Monday:
We went over homework problems.
We discussed the Rayleigh criterion, and solved some problem using it.
Wednesday:
We started studying electricity in general and Coulomb's law in particular. Coulomb's law
mathematically encodes the observations that there is a force between two charges which
may be attractive if there are opposite charges (one positive, the other negative) or
repulsive if the there are like charges. The force between two charges obeys a
so-called "inverse square law" which describe the way in which the force decreases as
the distance increases. An inverse square law is considered to be a long-range force. Another
example is the gravitational force between two masses, which plays a role on astronomical scales.
If electricity does not seem long range, it is because it often involves a nearly equal amount
of attraction and repulsion, which leads to cancellation in the superposition of the
individual forces.
Since Coulomb's law involves two charges, it is important to be clear which charge is feeling the effect
of a particular force, then the other charge is viewed as the source. Newton's third law implies
that each charge imposes a force on the other. The difference between these two forces is what they act on
and their direction. Their direction is given the unit vector r-hat. Think of the charge serving as
the source at the center of a polar coordinate system. Then r-hat lies along a radius from the source charge
to the second charge and points radially outward.
The unit for charge is the Coulomb (C). It is a large amount of charge, so one often sees
mC (milliCoulomb = 10-3C), μC (microCoulombs = 10-6C) and nC
(nanoCoulombs = 10-9C). The constant k is given by 8.99 X 109
N m2/C2. Because the constant involves meters, the distance between the charges
the r is the denominator) should be converted to meters.
We discussed symmetry as a problem solving technique.
We discussed electric field lines as a way of visualizing problems with a few charges
Electric field lines have a direction (and and generlly drawn with arrows).
Electric field lines start on positive charges.
Electric field lines end on negative charges.
Electric filed lines do not cross.
Electric field lines do not stop except on charges (otherwise the go off to infinity – or the edge
of the drawing).
