January 19, 1999.... Physics 201B... Spring 1999
Force between charges:
Force between masses:
G = 6.67 x 10-11 N m2 / kg2
k = 9 x 109 N m2 / Coul2
So how much charge must we put on two 1 kg masses to have the electric force = gravitational force? M=m= 1 kg; Q=q
G M m = k Q q
6.67 x 10-11 N m2 / kg2 * (1 kg)2 = 9 x 109 N m2 / Coul2 * Q2
Q = 8.6 x 10-11 Coul = 5 x 108 electrons
1 kg copper has approximately 3 x 1026 electrons.
But the biggest difference between the gravitational force and the electrical force is that M is always the earth so we can only vary m and its position r from the center of the earth ----- whereas in electricity, nature has not provided a single large charge Q so we are able to change BOTH Q and q as well as the distance r between them.
The Concept of a FIELD...
Recall the force between two masses, M and m:
Let us consider M as the mass of the earth and m is a mass near the earth ... we then rewrite the force as
where the term in parentheses called the field strength at a distance r from the mass M.... the strength at the surface of the earth is 9.8 N/kg or 9.8 m/s/s...
The direction of the field line at a point is the direction of the force that would be exerted on a mass at that point.
The field (g) is calculated at point P... IF a mass (m) is put at point P, then the mass feels a force (mg)... the field exists at point P due to mass M... Since forces are ON a mass... there is no force at P until the mass is put there. Note that the gravitational field for a mass always points toward the mass.
The same concept applies in Electricity... a charge Q creates a field...
and we rewrite this as...
and we note that the electric field strength has units of Newton/Coulomb (N/C)... If Q is +, the field points away from Q and if Q is -, the field points toward Q...
If we put a mass in a gravitational field and apply Newton's Law to it... we get:
If we put a charge in an electric field and apply Newton's Law to it... we get:
What happens when we move a mass through a gravitational field?... when we move a charge through an electric field?
If we move the mass m from a to b (a distance d) through the gravitational field, we do work (Fpath d) and the mass gets a change in potential energy. DPE = mg d
If we move the charge q from a to b (a distance d) through the electric field, we do work (Fpath d) and the charge gets a change in potential energy. DPE = qE d
We now define the change in potential energy per unit charge as the change in VOLTAGE. DV = DPE / q = E d.
Notice that DV has the units of Joules/Coulomb... Thus a 9 volt battery means that a coulomb of charge at the positive terminal of the battery contains 9 Joules of energy.
Where does the energy, that the charges have, come from???
Symbol for battery:
Now we can spread Q in whatever shape we want... for example, if we take two parallel metal plates and put positive charge (Q) on one plate and negative charge (-Q) on the other... we create a uniform field between the plates...
Suppose we shot an electron into the region between the plates as shown... which way would it go?
Suppose we shot an electron out of the paper into the regions shown... which way would it go?
An inside look at a TV... a love affair between unlike charges?
Another way to create electricity... but first lets get magnetic...
What makes some atoms magnetic?... iron, nickel, ... Let's first talk about CURRENT... the flow of charge...
where current is in units of amperes (coul/sec). Note that either negative charge or positive charge can flow. A positive charge flowing in one direction is equivalent to a negative charge flowing in the opposite direction. We DEFINE current as the direction in which positive charge flows.
When current flows in most metals, it is the electrons which carry the charge. The metal does NOT become charged when current flows because when electrons flow. There are always as many electrons in a section of wire as there are protons. In typical flow electrons move very slowly... (or order of cm/s).
A Current creates a magnetic field which circles around the wire. If you put the thumb of your right hand along the wire in the direction of the current, the magnetic field will circle the wire in the direction of your fingers.
Now determine the direction of the magnetic field in each of the cases shown.
And now explain why some atoms like iron are magnetic.
SO... electricity MAKES magnetism...
CAN magnetism MAKE electricity...
A moving charge makes magnetism... a moving magnet makes electricity...
While magnet moves to right, a current is caused (induced) in loop in direction shown. While magnet moves to left, a current is caused (induced) in loop in direction shown.
Check in each case the direction of the magnetic field caused by the induced current.
Applications: Motors, Generators, Transformers...
Circuits... Batteries... Resistors... Capacitors... Coils...
Energy given to charges in battery can be put into
Resistor... (friction of current) as thermal energy
examples... light bulb, toaster, heater...
Capacitor... (electric field energy)... charges stored
Coil... (magnetic field energy)... current flows
Alternating Current (AC) Circuits:
AC sources: 120 volts, 60 cycles/sec
Power supplied by AC source: P = V I
Applications to common circuits...