r is the distance between the source charge and the point of interest.
is the unit vector that points from the source charge to the point of interest
Every charged object is surrounded by a field given by this relationship. Every other charged
object in the universe can “read” this field and will respond to its information by feeling an
electric force. Objects without electric charge neither create nor interact with electric fields
(they can’t read the business cards).
In this chapter you’ll learn how to calculate the electric field produced by charged objects. In
the next chapter, you’ll learn how the electric field can be “sensed” by other electric charges
resulting in the electric force.
Charge and Charge Density
Macroscopic objects are normally neutral (or very close to neutral) because they contain equal
numbers of protons and electrons. All charged objects are charged because of either an excess
or lack of electrons. (It’s much easier to add or remove electrons from an object than trying to
add or remove the protons tightly bound inside the nuclei of its atoms.) Thus, the electric
charge of any object is always an integer multiple of the electric charge on an electron.
Because of its fundamental importance, the magnitude of the charge on an electron is termed
the elementary charge and denoted by the symbol e. In a purely logical world, the charge on
any object would be reported as a multiple of e. However, since the charge on a macroscopic
system can be many multiples of e, a more user-friendly unit, the coulomb (C), is typically
used to quantify electric charge. In this system,
Thus, you can consider the charge on an electron as an incredibly small fraction of a coulomb,
or a coulomb of charge as an incredibly large number of electrons.
In many applications, in addition to knowing the total charge on an object you will need to
know how the charge is distributed. The distribution of charge on an object can be defined in
several different ways. For objects such as wires or other thin cylinders, a linear charge
, will often be defined. This is the amount of charge per unit length of the object. If
the charge is uniformly distributed, this is simply
where Q is the total charge on the object
and L its total length. However, if the charge
density varies over the length of the object, its value at any point must be defined as the ratio
of the charge on a differential element at that location to the length of the element:
I will always use uppercase Q to designate the total charge distributed on a macroscopic object and
lowercase q to designate either an unknown charge or the charge on a point particle.