5. Electric Charges



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PHY1053 Notes Ch 15 – Electric Forces and Electric Fields
15.1 Electric Charges

Electric charge is a property of matter.

There are two kinds (flavors) of electric charge, positive (+) and negative (-).
For our purposes, protons have a positive charge and electrons have a negative charge. Neutrons have no charge.

The magnitude (amount) of charge of one electron is the same as the magnitude (amount) of charge of one proton, but they are opposite signs. So if you have 2 protons and 2 electrons together (like in a helium atom), the total charge is zero. This is like making a bank deposit of $200 (+200) and then making a withdrawal of $200 (-200). The result is zero.


Electrons and protons have very small amounts of charge, so the standard SI unit of charge, the Coulomb, is a much larger (but more useful) unit of charge. One Coulomb is equal to 6.25 x 1018  proton’s worth or electron’s worth of charge (depending on whether it’s positive or negative charge). So one electron has -1.6 x 10-19 Coulombs of charge and one proton has +1.6 x 10-19 Coulombs of charge. We will use “C” to represent Coulombs. So a carbon nucleus (6 protons, 6 neutrons) has 6 x (+1.6 x 10-19 ) = +9.6 x 10-19 C of charge.
Objects that have charge exert forces (pushes or pulls, measured in Newtons) on one another.

Like charges (positive and positive or negative and negative) repel each other.

Unlike charges (positive and negative) attract each other.
Newton’s 3rd law says that, if body A exerts a force on body B, body B exerts an equal magnitude but oppositely directed force on body A. So, if you have an electron and a proton out in space somewhere (or in your muscles somewhere),

the proton will attract the electron and the electron will attract the proton with the same amount of force. But, because



mass of a proton (mP = 1.67 x 10-27 kg), is much larger than the mass of an electron (me = 9.11 x 10-31 kg), the acceleration of the electron will be much larger than the acceleration of the proton, if both are free to move around, as per Newton’s 2nd law (ΣF = ma).
Charge is a conserved quantity, which means that, as far as we know, charge is never created or destroyed. So, if you have a helium atom (2 protons, 2 neutrons, 2 electrons), its charge is zero. If you somehow drag the electrons away from the nucleus, the two electrons will have a charge of -2, the 2 protons will have a charge of +2, and so the total charge is still zero.
Charge is quantized, which means that it always comes in units of 1 electron’s worth, or 77 electron’s worth, or 372 proton’s worth, but never 23.4 electron’s worth, or 1.7 proton’s worth. This is like eggs. You can buy one egg, or 12 eggs, or a gross (144) of eggs, but you can’t buy 3.7 eggs, or 123.47 eggs. I can have 24 students in a class, but I can’t have

23.7 students in a class. So, number of humans is also a quantized property.


15.2 Insulators and Conductors

In order to make charge useful to us, we usually have to make it move, often within a material (like copper wires or

muscle cells). Protons are massive and don’t move around much in most solids, but the electrons associated with the atoms can often move around because they are not so tightly bound to the atoms. In particular, the valence electrons of a material (those that are least tightly attracted to their respective nuclei) are most likely to move around in a solid. Materials where the valence electrons are not too tightly held to their nuclei (and are therefore relatively free to move around) are called electrical conductors (copper, aluminum and silver are good examples). Materials where the valence electrons are tightly held to their nuclei (and are therefore less free to move around) are called electrical insulators (rubber, wood and most plastics are good examples).
15.3 Coulomb’s Law

Coulomb’s Law tells us how strong the electric force is between charges. Here it is:
F = (k Q1 Q2 ) / r2
where Q1 and Q2 are the charges (in Coulombs), r is the distance between the charges, and k (the Coulomb Constant) is equal to 8.99 x 109 Nm2/C2.
So, for example, if a helium nucleus (Q = 3.2 x 10-19C) is 12 mm (12 x 10-3 m) away from an electron (Q = -1.6 x 10-19 C), the force will be F = (8.99 x 109 Nm2/C2) ( 3.2 x 10-19C) (-1.6 x 10-19 C) / (12 x 10-3 m)2 = 3.2 x 10-24 Newtons.
See examples 15.1 – 15.3 in the book for some other examples. Remember, these are forces, which are vectors,

so we have to take into account the components if we are doing a 2 or 3 dimensional problem (as in example 15.3).


Let’s notice several things. Firstly, force is a vector quantity (direction is important). So if several electric forces are acting on an object, in order to decide what it’s going to do (ΣF = ma), we first need to find the net force (ΣF) on the object (including direction) and then apply Newton’s second law (ΣF = ma) to determine its acceleration. (see ex 15.3). Once we know the acceleration (a), we can use the kinematic equations to know how the particle will move.
Secondly, notice that, since we have an r2 in the denominator, the electric force is an inverse square law (similar to gravity in physics I). So, if the charged objects are twice as far away from each other, the force is four times less, and if they are three times farther away from each other, the force is nine times less.
15.4 The Electric Field

The concept of electric, magnetic and gravitational fields is very useful in simplifying many problems. If you put a charged object (say a proton) somewhere in space (or in your liver) and that object feels an electric force, then we say there exists an electric field at that location. The electric field has a magnitude and a direction. The magnitude of the field is the force per unit charge that an electrically charged object will feel at that location. The direction of the field is the direction of the force on a positive charge. So we write


E = F/q
The unit for electric field is therefore Newtons per Coulomb (N/C). So if there’s a field with strength 1000 N/C and you put a proton there (q = +1.6 x 10-19 C), the proton will feel a force
F = qE = (1000 N/C) (+1.6 x 10-19 C) = 1.6 x 10-16 Newtons
Since we know the mass of the proton (1.67 x 10-27 kg), we can use Newtons 2nd law to find its acceleration. An electron would have a different acceleration, first of all because it’s negative and would go in the opposite direction, and secondly because its mass is much smaller than the proton’s.
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