The third and final fundamental force we will be discussing in this series is the magnetic
force. You may have noticed that although there is an electromagnetic force, I have divided the
two up into two different lessons. Though they are really the same force, some of the equations
are different, so it is easier to teach them separately.
You may have heard the term magnetic field, well in physics, a field of that sort is really
imaginary. It's really just the area around a magnet in which particles are affected. Although
there is really no distinct area, for ease in discussions someone came up with the term "field".
And for those same purposes, I will continue to speak in terms of the magnetic field.
The force exerted by a magnetic field upon a charge that enters it can be determined by the
equation:
FB = q * v * B * sin
In this equation, q is the charge of the particle, v is the velocity of the charged particle,
B is the strength of the magnetic field, and q is the angle between the field and the particle.
I know it sounds complicated, but it's really not that tough. You already know velocity,
and we studied charges in the last lesson, and we just discussed magnetic fields.
The magnetic field is measured in Tesla (T). The only other part of the formula that needs
explaining is where you get . is the
angle between the vector of the charged particle, and the direction of the magnetic field.
Although the particle can enter the field at any direction, for introductory purposes, we will
keep everything at a 90° angle.
The only thing left to mention before we get into a sample problem is the answer to the
question, "At which direction does the particle leave the field?"
To figure that out, we need a thing called the right hand rule. Form your right hand into a
gun, with thumb pointing up and index finger pointing straight out. Next, extend your middle
finger outward, so when looking down on your hand the index and middle fingers form a 90° angle.
You may be thinking, gee this looks cool, but what do I do with it? Good question. Pretend
that your middle finger is the magnetic field, and your index finger is the direction that the
particle is moving. The thumb represents the direction that the force is going. To help all of
this soak in, let's work an example.
What is the force experienced by a proton moving south at 7.5e6m/s in a region of the earth's
magnetic field that has a vertically downward component of 40mT? What is the direction of it's
deflection?
First, let's find the magnitude of the force.
FB = 1.602e-19C * 7.5e6m/s * 40mT * sin 90°
FB = 4.806e-17N
Now, let's figure out the direction. Place your right hand into the right hand rule
formation. Rotate your hand until your middle finger, the magnetic field, is pointing downward.
Next, move your hand until your index finger, the particle, is pointing south. (It doesn't really
have to be south, but you need some sort of a reference point to know where the rest of the
directions are) Then, just look at where your thumb is pointing. To the east, right? Good.
That's it, the force exerted upon the particle is 4.806e-17N, going east.
Now, for an negatively charged particle moving through the field, just reverse the answer
you get for a proton. For example, if the last problem had used an electron instead of a proton,
the final direction would be west, not east. Granted you can also use your left hand instead of
your right to come to the same conclusion, but I urge you to use your right hand. In later
physics classes you will learn cross products, which only use your right hand, so it will be
easier if you get used to using it now.
You've heard of forces, but in the next section you will learn
a new term, friction.
Fundamental Forces Sample Problems
