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Fields/Static Electricity, Coulomb's Law, Electricity and Magnetism

Keith Herold

on 23 March 2018

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Some postulates or givens that are important to remember:
1. energy can neither be created nor destroyed and and electric charge is the same {Law of
of Energy}
2. energy can change into other forms...
3. electricity is about electric charges (E-Z) both positive and negative
4. E is quantized...(what does that mean?)
Sample Question one in book:
two separated identical metallic spheres are charged with 4 & -12 uC respectively (I will use the u as a micro). They touch and now what is the Z on each sphere?
They end up with the same charge so it is the average of the two... (-12uC + 4uC)=-8/2=-4uC....

On a side note: there is no charge on the inside of a sphere. Like charges will migrate to the farthest point away from each other. In a sphere that is on the outside surface.
charging by friction -eg: silk and glass rod
charging by induction -eg: bringing a large negative charged object such as a balloon to a wall. Without touching! The wall will get its electrons pushed away creating a temporary dipole of positive at that specific point. The balloon will be attracted, being negative.
charging by conduction
The Earth is a giant storage container or "sink" for electricity. The potential is zero as the charges do not become unbalanced. Current or charges (unbalanced) will tend to flow into the earth. Allowing this is called grounding or "earthing''(from your book).
We can not forget vectors. Forces are vectors and need to be dealt with appropriately. The best way to refresh our memory of how to deal with the resultant addition of forces is to work a problem with three point changes (q's) in space and find the net force on one of the charges.
Here is a problem from Tsokos page 287 #7
q1= 3 uC is 3cm directly above q2=-3uC. q2=6uC and is 4cm directly to the right of q2. This forms a 3-4-5 triangle. Find the force on q1.
Know how to determine the charge on x-amount of electrons or how many electrons are in x-amount of coulombs...
e.g. If I have a 16 coulombs, how many electrons does this represent. WELL......
if 1 electron=1.602E-19 C /then x-electrons are in 16 C
or: 1e/x-e=16/1.602E-19
x=1.0E-20 electrons
Electric fields and strength
All electric charges create an electric field around themselves in space.
This electric field has a magnitude and is directional, so it is a vector.
Electric Field=force per unit charge.
E=F/q {units are NC^-1 or N/C}
When we check the strength of an electric field we use small test charges so as not to disturb other charges entities around in the area.
If I substitute kqq/r^2=qE the equation reduces out one of the q's and E is left on one side to equal the Electric Field strength from Coulombs law for a single point charge is E= kQ/r^2
In electrostatics, the electric field inside the conducting body is zero. Static charge doesn't move so having a force inside would imply there would be charges moving...
Electric field lines diminish exponentially out from the source. Know how to draw field lines.
Electric potential: potential to do work! V=W/q V is voltage, W=work, q is the charge in question.
"measure of the electric potential transferred from an electron when it is moving between two points in a circuit.
The work done in moving a test charge from far away from a charge can be calculated. The test charge=5.0uC and the work done is 175x10^-6 joules (J). What is the potential at the test charge now?
V=175x10^-6 J/5.0x10^-6C
V=35 volts (V)

*The volt is a joule/Coulomb
The concept of Potential difference
is different from the field around a charge we call this electric potential, potential difference or voltage.
Potential difference implies you must have changed the position of the charge and the amount of potential in relation to a point test charge or another charge has changed. So the potential work has changed...
A new potential difference has been created.
CONSIDER if I have a charge {=2 coulombs} at position A of electric potential of 15v and move this charge to a new position, B, & its' new electric potential has changed to 28v, what work was done on this charge?

So at position A.....
V=W/q so therefore W=V x q = (15V)(2C)=
=30 J

At position B
W=V x q = (28V)(2C)=
=56 J
Therefore the change in potential Energy = the difference
in Work energy is 56J-30J=
=26 J
PLATES: AND THE electric fields and discharged speeds between them.
Work done on moving a charge across a plate is:
simply knowing the voltage potential difference and the charge.
e.g.A 5.0uC charge is moved across two plates where the potential diffence (voltage) is 250 volts, What is the Work done? since V=W/Q so W=V x (q)

1.25E-3 J
As a class we will now move onto Electric Current and electric resistance. A new Prezi will be made...
-The End-
Newton's 2nd: F=ma
Nb: if we take the Univ. Law of Gravit. and find Force, we can then find the acceleration due to gravity. Note that the radius of an object is to the center of the earth or what ever planet we are dealing with.
So if you had a 1kg mass 100.0 meters above the moon, what acceleration will be experienced if it is dropped?
Moon's mass is 7.35E22 kg and the radius is: 1737.4 km
Volunteer please on board......

Since objects with mass attract each other without being in contact we must consider the space between them.
A region where you find gravity=the gravitational field. This is a vector quantity.... little g.... since F=ma or =mg g=F/m N/kg or kg m/sec2 per kg so kg's cancel and we get m/s^2
Little m cancels
of mass
sphere with electrical Z
and point Z's
Work in Kinematics is similar but not calculated the same. Units are still in Joules though. W=force x distance and if an incline Force x dist. x cos theta
In Electrical systems: 1 Joule is 1 coulomb thru a potential difference of 1 volt. J=C/V

One Coulomb of q = 6.25E18 electrons.
One electron has a q= 1.6E-19C
So if you have a single point charge with a value of +40 uC, you can calculate the field strength at any location away from it... e.g. at 4cm away.
E=k q/r^2 E=(8.99E9)(40E-6C)/(0.04m)^2
=2.25E8 N/C
LAW OF CONSERVATION: states that in a closed
system the amount of charge is constant. i.e. charges are
conserved (not lost).

charges are either positive or negative
electrons make up electricity and in the Data Booklet under Fundamental Constants are listed as the "Elementary charge" of one electron "e" =1.6 E-19 C's

1.6x10^-19 Coulomb's: *this is the charge of one electron...
1C= 6.25E18 electrons (not in Data booklet)
this is a lot of electrons!
Commonly we think of electrons as carrying the electric current along or the flow of electrons. But...in liquids and gases +ions can also transport charge.
"The coulomb is defined as the charge transported by a current of one ampere in one second"

If you have the same # of negative charges (e's) and positive charges you are neutral.
induction-not touching

Insulators vs. Conductors
pure water
dry wood
water with ions in it
some non metals such as carbon silicon

What is the definition of a coulomb of charge?
---->the charge transported by a current of one ampere in one second
===amperes or amps is the current; the larger the flow of electrons the greater the amperage or more amps.
*there are smaller things then electrons.
Quarks have fractional charges of +/- 1/3 e, and +/- 2/3 e.
But not ever observed outside of the nucleus of atoms in their nucleons (protons and neutrons). Both protons and neutrons made of 2 quarks up=+2/3 q and down=-1/3 q.
----described by Coulombs Law

the force is directly proportional to the product of the charges and inversely to the distance between them.
F=k q q/r^2
k=Coulomb's constant
when using the k use the value 9X10^9 Nm^2C^-2
Note (Nb:) in the textbook see how permittivity is different for different mediums but air is so close to the value that of a vacuum with use the k value for both.
In D.Booket fundamental constants given that E=8.85 X 10^-12 C^2/Nm^2
So therefore 8.99X10^9 is = 1/4phiE !
Van der Graaf Generator
-how does it work? can you explain it?
Go to worked problem page 179 in Oxford textbook.
Dr. H--please put it up on the screen with document camera.
Amperes is the unit (A) or Amps.
Current is how much charge is passing by per second.

I=change in Q/change in time t
freq=cycles/sec or 1/T so T=1/freq.
What is Drift Velocity?
the speed of electrons due to the current
What is conventional current?
by convention we use the wrong explanation of charge movement through a conductor.
flow of + charges moving
electrons actually move opposite to the direction of conventional current!
pd=pot. diff. = Voltage V
Next we go to current example.
A new PREZI will be made from this point on.
Electromotive Force (emf)
when charges flow electrical energy changes in the circuit.
energy can change form and be transferred such as heat or light.
used often in describing an energy source such as in batteries, e.g. : 1.5 V

See worked example page 175 Oxford #2 when not in a vacuum and permittivity is different.
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