Could Tesla’s long-distance, wireless power transmission system have really worked? Many people believe this, and there have been an incredible number of conspiracy theories concerning this topic. However, Tesla’s work in this area was publicly demonstrated and well documented. Also, since his time thousands of scientists and engineers have also investigated how radio waves transmit electrical power. We can read about the results here: Tesla and wireless power transmission.
32.1 Electrical forces and charges
We’ll use the “solar system” model of an atom.
This model is useful for understanding electrostatics,
and for most of high school chemistry.
Caution: the atom isn’t really like a solar system at all.
Saying so is just a sometimes-useful-analogy.
The solar-system model often lets us find useful answers, to a huge number of practical problems.
That’s awesome. That’s why we use it.
Yet in other cases its predictions fail.
Sometimes, it’s predictions fail spectacularly!!!
When we get to the section on Modern physics we’ll discover why.
For now, just know that the solar system model is an often useful analogy, but not literally correct.
If you want to get ahead you can read about the development of the modern understanding of the atom.
Solar system model of the atom:
Viewing the atom’s sub-atomic particles.
Opposites electrical charges attract. Like electrical charges repel.
Conservation of charge
In neutral atoms, we have the same # + and – charges.
If we add or subtract electrons then the atom is no longer neutral – and it’s behavior changes radically. When this happens it is known as an ion.
Ions do not have same # of + and – charges.
In theory, one could add or subtract protons, but experiment shows that no chemical reaction can do this. In fact, if one could change the number of protons, then one would literally have a different kind of atom (for example, turning lead into gold.) Under any kind of normal circumstance, that is literally impossible.
In the section on Modern physics we will discover, however, that under amazingly extreme circumstance – such as inside a star – atoms can change the number of protons, through nuclear fusion.
Electrically charged objects
Conservation of charge: electrons are neither created or destroyed – they simply can move from one place to another.
Only entire electrons can be transferred – they cannot be broken into smaller pieces.
In 1784 French physicist Charles Augustin de Coulomb discovered how strongly charged objects attract, or repel, each other.
Just like gravity, their force follows an inverse square law.
If charges are opposite – they attract
If charges same same – they repel
How strong is this Force? Depends on r (their separation)
Hmm – depends on r … the inverse of r?
How about – the inverse of r squared !
Let’s plot the force between two charges, at different distances:
Put in some number for q1 (charge on object 1) and q2 (charge on object 2.)
Set “k” to the strength of electrical interactions in our universe.
(How do we find this number? That’s another story!
For now, we’ll just give it to you )
Now plug-and-chug: Change r , and see what the resulting force is.
We end up with this graph.
Notice how as the distance shrinks, the force drastically increases?
(Or, as the distance increases, the force drastically drops?)
You might ask – what is “k”? Just some random number?
No my friends, it is so much more!
K is a fundamental constant of nature:
it is something inherent in the fabric of reality itself
it sets the strength of how strongly charged objects attract/repel.
Mathematically, how does “k” function?
It alters the shape of the hyperbola, as seen above.
When we set “k” to it’s true value, we get the blue curve (above)
If k drops by an order of ten, we get the orange curve.
If k increases by an order of ten, we get the gray curve.
What is a coulomb? (unit symbol: C)
It is the SI (Metric) unit of electric charge.
It’s symbol is either Q or q.
1 coulomb = # of electric charges transported by a current of 1 ampere, in 1 second
HUGE NUMBER ALERT
6.2415 × 10 18 protons or electrons.
We can imagine electrical current looking like this: Red circles are metal atoms – including the nucleus, and almost all of the electrons. Smaller moving circles are valence electrons that are not tightly bound to any one atom.
coulombs -> amount of charges
amperes -> flow of charges
If you rub two different fabrics together, you might get a static electric shock.
How much electrical charged when this happens?
Only a very tiny amount, even for a large shock.
1 microcoulomb = 1 μC = 1 x 10 -6 C
So how much charge is on just one electron,
compared to a coulomb of charge?
e = 1.602 x 10 -19 C
Let’s look at the equation again:
hmm, the electrical force law has the same form as the law for gravitational force!
How are they different? Gravity has to be attractive. (no such thing as anti-gravity)
Electric forces can be attractive or repulsive.
proportional constant “k” for electricity is enormously high.
proportional constant “G” for gravity is enormously low.
Electrical forces in atoms
Atoms may even share electrons.
Do the math!
Conductors and Insulators
Electrons are more easily moved in some materials than in others.
Here’s a neutrally charged conductor – and its response to charged objects being brought near it.
Electrons are free to to move around within the conductor. They have a “sea of electrons”.
As the + charged rod is brought near, electrons are attracted toward the rod. This causes a force of attraction to be created between the rod and the conductor.
As the – charged rod is brought near the conductor, the electrons are repelled away from the charged rod. This causes a force of attraction to be created between the rod and the conductor.
As a result, we can say that a charged object will always be attracted by a conductor.
Only valence electrons are free to move: the rest of the atom [protons, neutrons, inner electrons] are fixed in place.
Notice that when no charged object is near the conductor, the electrons evenly distribute themselves within the conductor.
This is a neutrally charged insulator and its response to a charged object being brought near it.
The electrons are not free to move – they are generally restricted to moving only around the atom they’re attached to. Charges stay where you put them on an insulator.
Here electrons are evenly distributed, but still attached to only one of the positive charges. As the negatively charged rod is brought near, notice that the electrons move to the other side of the positive charges – but are unable to move completely to the far side of the object.
Even though the charges only move to the other side of the atom, the upper side of the insulator becomes more positive – it therefore feels a force of attraction to the the charged object.
(There would also be an attraction if the object was positively charged.) As a result, we say that a neutral insulator will always be attracted to a charged object.
The speed of electrons in a conductor
In electronic devices, the signals/energy travel as electromagnetic waves: very, very fast. Typically around 50%–99% of the speed of light!
But the electrons themselves move (drift) much more slowly, as slow as 1/1,000th of a meter/second.
How can the energy travel quickly, while the individual electrons travel so slowly? Let’s look at a longitudinal wave – how can this help us understand?
Charging by friction and contact
As the neutrally charged person walks across the wool carpet, his leather soled shoes have less desire for electrons than the wool carpet.
As a result, electrons get stolen from the shoe by the carpet.
With every step he becomes more + positively charged. That charge distributes itself over the body.
When the + charged person gets near the metal door, these charges attract opposite ( – ) charges from the door:
they jump in the form of a spark.
Notice how only the negative charges (electrons) are free to move.
Notice that the spark is MOVING electrons. They are “dynamic”, not “static” (the word ‘static’ means not moving) Thus physicists note that the name for this phenomenon is a misnomer.
If he was wearing rubber soled shoes on a wool carpet, then his shoes would steal electrons from the carpet. He would become more negatively charged with each step. When he gets near the door the electrons will jump from him to the door.
Yet it would look/feel the same as it did in the first example. He can’t tell whether charges jumped to or from him.
text above adapted from Science Joy Wagon 1999
Can we use “static” charges on an item to polarize atoms in the wall, and stick a balloon to it? Yes
Charging a balloon with friction, and then sticking to the wall
Notice how the unbalanced electrical charges in the balloon cause the charges on the wall’s surface to (slightly!) move? Polarization
Can we use “static” charges on an item to polarize atoms in cat fur,
and stick a balloon to it? Yes
Can we use “static” charges on an item to polarize atoms
in a stream of water, and pull the water? yes
Charging by induction
Image below from Charging a Two-Sphere System by Induction Using a Negative Object
Contrast : charging by Conduction, and by Induction
These images are from Charging by Electrostatic Induction: Science Joy Wagon
Charged object touches the electroscope.
Electroscope ends up similarly charged to the object used to charge it.
The first charge is strong but gets weaker each time the electroscope is recharged. (original object is giving up some charge every time it is touched.)
Charged object does not touch the electroscope.
Electroscope ends up oppositely charged to the object used to charge it.
The first charge is strong and stays strong each time the electroscope is recharged. (original object not losing any charge in the process.)
32.7 Charge Polarization
Many molecules are normally electrically polarized
Conceptual Physics PowerPoints PowerPoints by Book and Chapter
HS-PS2-4. Use mathematical representations of Newton’s law of gravitation and Coulomb’s law to both qualitatively and quantitatively describe and predict the effects of gravitational and electrostatic forces between objects.
HS-PS3-2. Develop and use a model to illustrate that energy at the macroscopic scale can be accounted for as either motions of particles and objects or energy stored in fields [e.g. electric fields.]
HS-PS3-5. Develop and use a model of magnetic or electric fields to illustrate the forces and changes in energy between two magnetically or electrically charged objects changing relative position in a magnetic or electric field, respectively.
Learning Standards: Common Core Math
- CCSS.MATH.CONTENT.7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
- CCSS.MATH.CONTENT.8.EE.C.7 Solve linear equations in one variable
- CCSS.MATH.CONTENT.HSA.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (including isolating a variable)
- CCSS.MATH.CONTENT.HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.