13.8. What to Remember from Lesson#
13.8.1. Fields#
The notion of a field is critical for us. In essence, a field is a disturbance in space which links together a cause and an effect. In electricity, the cause might be an electrically charged object and the effect – some distance away – might be a force that a different electric charge might feel. The disturbance between them is the Electric Field. This field idea will receive corrections when we get to quantum mechanics, but this image is a pretty reliable one.
BTW. This worked so well for electricity that we certainly also think of a gravitational field – another “disturbance” where the source might be some mass like a planet or an apple and the effect would have to be some other mass. The force that the “effect” mass feels, unlike in electricity, is always attractive.
There are two kinds of fields, those in which one can assign just a number (with some units) to every point in space. The temperature field on TV is the perfect example and when direction doesn’t matter, we call these “scalar” fields.
The other kind of field is one in which not only can you assign a number to every point in space, but also a direction associated with that number. Again, the weather is the perfect example where the distribution of winds is such a field, called a “vector” field. The Electric and Magnetic fields are both vector fields, where the direction and the magnitudes are a little harder to get a feel for.
13.8.2. Electric Field#
We know that the electric field is a real thing because not only does it make a cause and effect relationship happen, but between the two objects, one can tickle the space with another charge and watch it move. By carefully watching what direction a little test electric charge is moved and the force that it feels, one can map out the force field.
But the force that a test charge would feel depends on the charge of the source and the charge of the test field. It’s not useful to have a physical quantity’s value depend on the probe so…we divide it out leaving a quantity that is only related to the source itself. So for a point electric charge of \(Q\), the force that a little test \(q\) would feel is:
So if we divide out the little \(q\) we create a quantity that we define to be the Electric Field, \(E\):
Now it doesn’t matter if the test probe is \(q=1\) or \(q=50\), the result for the value of the Electric Field is the same.
Many different real electronic components are constructed from engineered arrangements of electric charges. We’ll consider only:
point electric charges, singly and in pairs
lines of electric charges
sheets of electric charges
two parallel sheets of opposite electric charges
The shapes of the resulting electric fields are shown in the text.
13.8.3. Energy in Electric Fields#
Here’s one of our mantras:
If there is a force, then there’s an acceleration
If there’s an acceleration, then there’s a change in velocity
If there’s a change in velocity, then there’s a change in kinetic energy
So somehow when an electric charge is dropped into an electric field it will gain kinetic energy and above we learned that for a uniform electric field, \(E\), the kinetic energy that any charge \(Q\) would gain as it experiences the electric force through a distance \(x\) would be
(Notice that’s a force times a distance, which is work.) Where does this new energy come from? From the electric field itself. Electric fields store energy and can transmit energy.
It’s also useful to think of the fields ability to perform work on a charge…where I’ve intentionally appropriated the language we used in Lesson 7. The field is fixed and through some distance \(x\) the amount of energy gained depends on the charge that’s put into the field. So a big charge would experience a large kinetic energy and a small one, less. But what’s constant – what’s Potentially possible doesn’t depend on the charge, but only the value of the field and the distance. So we speak of a Potential Energy per unit charge and give it a name that you know: Volts (V)…which is also Joules/Coulomb.
This in turn leads to a practical unit for the electric field of Volts/meter in addition to Newtons/Coulomb.
13.8.4. Electron Volts#
Coulombs is an old unit that stuck around. It came from the time when people were fretting over electrically charged big objects. Now we know that these big objects had an enormous number of our fundamental atomic electric charge of \(e=1.6 \times 10^{-19}\) C. Those \(10^{-19}\)’s are just arithemetic mistakes waiting to happen, so we have invented another unit more applicable to atomic physics and chemistry: the electron-volt.
A single electron volt is the amount of energy that a fundamental charge, like a proton or electron, gains while being accelerated through a potential of 1 Volt. That number is:
13.8.5. Magnetic Fields#
Just like there is a definition for the electric field, there is one for magnetic fields. These are a little harder to calculate and so we’ll leave it at the picture level, where the whole point of a magnetic field is that a current causes a magnetic field to be produced around the wire, according to the right hand rule: put your thumb in the direction of the current and your fingers will curl around in the direction that the magnetic field points – for your right hand only. A number of pictures of different magnetic configurations are above and the only ones that we’ll care about are:
the magnetic field of a single wire
the magnetic field of a current loop
the magnetic field of a solenoidal current
the magnetic field of a torridal current