The next force we are going to discuss is the electric force. The equations for the
electrical and gravitational forces are basically the same, except that there's a different
constant and we are using charges instead of mass. Here's the equation:
(k * q1 * q2) / r2, where k is the electric constant and q1 and q2 are the charges of the
particles.
The constant k is equal to 8.988e9Nm2/C2, which again is just for calculation purposes, but
I will just write k in my equations. Also, the charge for either a proton or an
electron is 1.602e-19C, where C is the unit Coulomb. The main difference when
working problems using electric or gravitational forces is that with gravitational forces the
objects always attract, where as with electric forces it all depends on the particles. Like
particles attract, while differing particles repel.
Many times you have probably seen or heard protons referred to as positive, and electrons
referred to as negative. In reality, they aren't really positive or negative, the signs are
just a way to differentiate between them. If you see a problem that has a 1.6mC charge, you
know it's protons; where as you if you see a problem that has a -6.8mC, you know it's full of
electrons. The signs have no bearing on the actual calculations. Let's work a sample problem:
A 2.2mC charge is located on the x axis at -1.5m. A -5.4mC charge is located on the y axis
at 2.0m. A 3.5mC charge is located at the origin. Find the net force on the 3.5mC charge.
First, let's draw a picture.
Next let's calculate the charges.
FE = (k * (2.2mC) * (3.5mC)) / (1.5m)2
FE = 3.076e-2N
FE = (k * (5.4mC) * (3.5mC)) / (2m)2
FE = 4.247e-2N
Since the charge to the left of the 3.5mC charge is also positive, the 3.5mC charge is going
to repel and travel to the right; and, since the charge above the 3.5mC is negative, they are
going to attract making the 3.5mC charge go up. Now, this is where a force diagram becomes
useful. It helps us keep track of the repelling and attracting forces and what the net force
ends up being.
Now we just need to combine the vectors and find the resulting force.
sqrt ((3.076e-2N)2 * (4.247e-2N)2) = 1.306e-3N
tan-1 (4.247e-2N / 3.076e-2N) = 54.085°
So, the net force is 1.306e-3N at 54.085°.
In the next lesson we will be discussing the last of these three
fundamental forces, the magnetic force.
