Website Notes: Fields (Part 2) - Electric Fields.
INTRODUCTION: In ancient Greece, amber became widely valued around
1600 BC. Greeks were fascinated by it. The ancient Greek word for amber
is "elektron", meaning - originating from the Sun. The Greeks were also
the first to describe the electrostatic properties of amber. Ancient Romans
loved amber as well. From the writings of Thales of Miletus it appears that
Westerners knew as long ago as 600 BC that amber becomes charged by
rubbing. There was little real progress until the English scientist William
Gilbert in 1600 described the electrification of many substances and coined
the term electricity from the Greek word for amber. As a result, Gilbert is
called the father of modern electricity.
One of nature's most spectacular display of electricity is the lightning
observed during a thunder storm. Benjamin Franklin (1706-1790)
found that electricity originates from charges, positive or negative. We
know now that all material bodies possess electric charges. Electrons
carry negative charges while protons carry positive charges in the nucleus
of an atom.
1. The electric force that stationary objects exert on each other is called
the electrostatic force. This force depends upon the distance between the
two point charges and the amount of charge on each. Experiments have
demonstrated that the greater the charge and the closer they are to each
other, the greater the force.
2. If charges have unlike signs, each charge is attracted to one other,
whereas like charges repel each other. These attractive forces and repulsive
forces act along the line between the charges, and are equal in magnitude
but opposite in direction (in accordance with Newton's 3rd law).
3. The French physicist Charles-Augustin Coulomb (1736-1806)
experimented with electric force between two point charges (the unit of
charge is the Coulomb, C). His work resulted in a law. Coulombs Law is
defined: The magnitude of the electrostatic force (F), exerted by one point
charge on another point charge is directly proportional to the magnitudes
of the two point charges, and inversely proportional to the square of the
distance (r) between the charges.
4. For a pair of charges q1 and q2, separated by a distance r, Coulomb's Law
may be stated as follows: F = k(q1q2/r2).
5. The constant of proportionality, k = 8.99x109 Nm2/C2. Such a force is
transmitted by the presence of an electric field. The electric field E due to a
point charge q is, E = F/q , or E = k(Q/r2).
6. Electric force and electric field are vectors. Hence, they have magnitudes
and directions. The electric force F and electric field E are related as follows:
F=qE, where the force is on charge q due to the presence of an electric field
at the position of q.
7. When an electric field is confined between two parallel metal plates, the
field is given by E = σ/εo, with σ, being the surface charge density, and εo
is the Permittivity of Free Space, or εo = 8.85x10-12 C2/Nm2.
8. The Principle of superposition also applies to the electric fields produced
by multiple charges. That is, the net electric field at a point due to several
charges is the vector sum of the electric fields due to individual charges.
9. For example, when more than two charges are present, the net force on
any one charge is equal to the vector sum of each of the forces produced by
10. In other words, the force on charge q1 due to the presence of charges q2
and q3, is the superposition of the forces exerted by q2 and q3. That is, the
net force F on charge q1 is, Fnet = F12 + F13.
where, F12 is the force on q1 due to the presence of charge q2 and F13 is the
force on q1 due to charge q3.
11. While solving a problem, it is useful to rewrite equation given above in
its component form as follows:
Fx = (F12)x + (F13)x
Fy = (F12)y + (F13)y
Fnet = [(Fx)2 + (Fy)2]1/2
θ = tan-1 [Fy/Fx]
12. And still, we need these steps to solve any problem in Physics:
(i) read the problem and identify the given variables
(ii) determine what you are asked to solve for
(iii) find the correct equation to use
(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown
(v) substitute-in the given information and simplify.
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