Electric Field Due Continuous Charge Distribtuions
"
Common sense is the collection of prejudices acquired by age
eighteen"
Albert Einstein
Electric charge is a property of individual particles -
protons, electrons etc. But since these particles are
extremely small it is often convenient to consider charge to be
continuously distributed.
These distributions can be over a line (one dimension), an
area (two dimensions) or a volume (three dimensions).
In order to determine the electric field due to a continuous
charge distribution we "sum" the fields due to the individual
"elements" that comprise the distribution, by integrating over
the line, area or volume in question. For example in the
example below charge is distributed uniformly over the rod on
the x axis. To determine the electric field at point P, we
write down the expression for the field at P due to the "point"
charge dq located at "x" as shown, then integrate over x from x
= 0 to x = x.
Overheard after a student failed a
physics test miserably:
Nuclear, Hydrogen, Atomic, My test- They can all be bombs.
