Download Sep. 28 - Bryn Mawr College

Physics 103, September 28, 2007
What we talk about when we talk about electricity (HLA § 6).
• Things have charge. This causes things to be attracted to and repelled by other things.
This is called the electric force. It is one of four fundamental forces in nature (along
with gravity, the weak force, and the strong force). Charge is labeled by q and has
units of Coulombs.
• Charge flowing through something is current; specifically, current is charge per time,
I = q/t.
• When calculating forces related to charged particles, it turns out to be extremely useful
to break things up into two parts: (i) Every charge produces electric fields which radiate
outward to all points in space (+ charge) or inward from all points in space (− charge).
The total electric field at any point in space is the sum of the electric fields due to all
particles. It is a vector sum, but we won’t worry about that. Electric field is designated
by E and has units of N/C or V/m. (ii) Once you know the total electric field at some
point in space, you can calculate the force on a particle of charge q; it is F = qE.
• When calculating energies related to charged particles, it is also useful to break things
up into two parts: (i) A charged particle produces a voltage, also called a potential, at
every point in space. The total voltage at any point in space is the sum of all voltages
due to all particles. Voltage is designated by V and has units of volts. (ii) Once
you know the voltage at some point in space, you can find the potential energy of a
charged particle placed at that point. It is U = qV . Potential energy can be converted
to kinetic energy, and vice versa, just as was the case for gravitational potential energy.
• A single point charge has electric field and potential:
E = kc
q
r2
V = kc
q
r
The Coulomb constant, kc , is 9 × 109 N m2 C−2 .
• In the space between two uniform, oppositely charged plates there is a constant electric
field, pointing from the + plate to the − plate. The voltage is lowest close to the −
plate, and it increases linearly with distance going up to the + plate.
• Electric charge comes quantized in units of e = 1.6×10−19 C. The charge of an electron
is −e. The charge of a proton is +e. The electron charge the subject of a future chapter
(§ 8.4).
Continued on the other side....
Beware
• I’ve never seen the constant in the electricity formulas written as kc before. Many
texts write it as k. But kc is perfectly fine, so we will use it in this class. As the book
1
mentions, professional physicists and engineers usually write 4π
. This crazy-looking
0
notation actually makes a lot of sense when one is doing advanced work, but it would
add nothing to our understanding of the material, so we won’t use it. As the book also
mentions, sometimes units are rigged so that kb = 1. One unit system that does this is
called “cgs units” because it is based on centimeters, grams, and seconds, rather than
meters, kilograms, and seconds. (The real distinction between cgs and mks is in how
they handles charge, not how they handles length, mass, and time.) In some branches
of theoretical physics, it is standard to use a system of units in which the speed of
light, Newton’s gravitational constant, and Plank’s constant are all 1: G = c = h = 1.
• Feel free to ignore the discussion of Coulomb’s experiment on pp. 135-136 of the text,
particularly the paragraph with a quantitative description of his results just before
Exercise 2. This is actually a pretty cool experiment, but it is also a little convoluted
(and the results are described in a confusing way in the text). If you want help
understanding what’s going on here, we can talk it through outside of class.
• Please, ignore the second paragraph on page 148, in which you are asked to visualize
electric potential as water vapor. This analogy is misleading.
Some problems we might work through in class.
1. HLA Problem 6.2
2. The force between two charges 2 m apart is measured to be 3 N.
VVhatwill be the force between the charges if they are moved to be
2
~
a.
m apart.
b. 6m apart?
3"
2. Imagine that all the electrons in your body suddenly disappeared, and that all the
electrons in the chair that you are sitting on suddenly disappeared, so that both you
and the chair were positively charged. Estimate the electrical force on your body which
would result from this situation. How does it compare to the gravitational force on
your body?
3. A metal sphere has a charge of 1 mC spread uniformly over its surface. What is the
strength of the electric field 1 cm away? What is it 1 m away? What is the force felt
by an electron at each of these positions? What about a proton?
4. Why do the pie plates fly off the Van de Graaff generator?