EP 104
General Physics II
CHAPTER-1
Chapter
1
Charge and Matter
There are two kinds of electric charges, which
were given the names positive and negative by
Benjamin Franklin (1706–1790).
One can identify negative charge as that type
possessed by electrons and positive charge as
that possessed by protons
When a glass rod that has been rubbed
with silk is brought near the rubber rod, the
two attract each other (Fig.a). On the other
hand, if two charged rubber rods (or two
charged glass rods) are brought near each
other in Fig.b, the two repel each other.
It is concluded that charges of the same sign repel one another and
charges with opposite signs attract one another
Electric charge is always conserved in an
isolated system.
When one object is rubbed against
another, charge is not created in the
process.
The electrified state is due to a transfer of
charge from one object to the other. One
object gains some amount of negative
charge while the other gains an equal
amount of positive charge.
When a glass rod is rubbed with silk, electrons are transferred from the
glass to the silk. Because of conservation of charge, each electron adds
negative charge to the silk, and an equal positive charge is left behind on
the rod.
The electric charge q is said to be quantized,where q is the standard
symbol used for charge as a variable. That is, electric charge exists as
discrete “packets,” and we can write:
The electron has a charge -e and the proton has
a charge of equal magnitude but opposite sign
e. Some particles, such as the neutron, have no
charge.
Electrical conductors are materials in
which some of the electrons are free
electrons that are not bound to atoms
and can move relatively freely through
the material;.
Electrical insulators are materials in
which all electrons are bound to atoms
and cannot move freely through the
material.
Semiconductor is a third class of materials,
and their electrical properties are
somewhere between those of insulators
and those of conductors.
Silicon and germanium are well-known examples of semiconductors commonly
used in the fabrication of a variety of electronic chips used in computers, cellular
telephones, and stereo systems.
Charles Coulomb (1736–1806) measured the
magnitudes of the electric forces between charged
objects. Coulomb’s law as an equation giving the
magnitude of the electric force (sometimes called the
Coulomb force) between two point charges:
where ke is a constant called theCoulomb
constant
permittivity of free space
The smallest unit of charge e known in nature is the charge on an electron
(- e) or a proton (+e) and has a magnitude:
The electron and proton of a hydrogen atom are separated (on the
average) by a distance of approximately 5.3x10-11m. Find the magnitude of
the electric force between the two particles.
Force is a vector quantity . The law expressed in vector form for the
electric force exerted by a charge q1 on a second charge q2, written
F12, is:
The electric force obeys Newton’s third law, the
electric force exerted by q2 on q1 is equal in
magnitude to the force exerted by q1 on q2 and in
the opposite direction.
The force F21 is the force exerted by q2 on q1
If four charges are present, then the resultant force
exerted by particles 2, 3, and 4 on particle 1 is:
Consider three point charges located at the
corners of a right triangle as shown in Figure,
where q1=q3=5.0µC, q2 =2.0µC, and a=0.10m.
Find the resultant force exerted on q3.
The force F23 exerted by q2 on q3 is attractive because q2 and q3 have
opposite signs. The force F13 exerted by q1 on q3 is repulsive because
both charges are positive.
The magnitude of F23 is:
The magnitude of the force F13 exerted by q1 on q3 is;
x and y components of the resultant force acting on q3:
the resultant force acting on q3 in unitvector form as;
Three point charges lie along the x axis as
shown in Figure. The positive charge
q1=15.0µC is at x=2.00m, the positive
charge q2=6.00µC is at the origin, and the
resultant force acting on q3 is zero. What is
the x coordinate of q3?
From Coulomb’s law, F13and F23 have magnitudes
the resultant force on q3 to be zero, F23 must be equal in magnitude and
opposite in direction to F13
This can be reduced to the following quadratic equation:
Solving this quadratic equation for x, the positive root is:
Two identical small charged spheres,
each having a mass of 3.0x10-2 kg,
hang in
equilibrium as shown in
Figure. The length of each string is
0.15m, and the angle is 5.0°. Find
the magnitude of the charge on each
sphere.
The free-body diagram for the
sphere on the left:
Because the sphere is in equilibrium, the forces in the
horizontal and vertical directions must separately add up
to zero:
From Equation (2), we see that:
T can be eliminated from Equation (1):
The separation of the spheres is 2a=0.026m, the magnitude of the
electric force is:
the charge is the same on both spheres