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- 1. CHAPTER 1:ELECTRIC CHARGE AND ELECTRIC FIELDS i)
Electrostatic ii) conductors and insulators iii) Coulombs Law iv)
Electric Fields v) Electric Fields Calculation vi) Electric Field
Lines vii) Electric Dipole1.1 ElectrostaticElectrostatic is a study
on the electric charges in thestatic or steady state condition. In
this chapter, we willdiscuss the basic and the fundamental concept
of electriccharges, electric fields and their
characteristics.Plastic rods and fur are good for
demonstratingelectrostatics.Benjamin Franklin (1706-1790) suggested
chargesnegative and positive.
- 2. Two positive charges or two negative charges repel each
other. A positive charge and a negative charge attract each
other.Caution: Electric attraction and repulsionThe attraction and
repulsion of two charged object aresometimes summarized as like
charges repel, andopposite charges attractBut keep in mind that the
phase like charge does notmean that the two charges are exactly
identical, only thatboth charges have the same algebraic sign (both
positiveor both negative). Opposite charges mean that bothobjects
have an electric charge, and those charges havedifferent sign (one
positive and the other negative).
- 3. 1.1.1 Electric charge and the structure of matterThe
structure of atoms can be described in terms ofthree particles: the
negatively charged electron, thepositively charged proton, and
uncharged neutron (Figabove).Proton and neutron in an atom make up
a small, verydense core called the nucleus. (10-15 m)Surrounding
the nucleus are the electrons(10 -10 m a far from nucleus).
- 4. The negative charge of the electron has exactly themagnitude
as the positive charge of proton.1.1.2 Electric Charge is
ConservedPrinciple of conservation charge: i) The algebraic sum of
all electric charges in any closed system is constant ii) The
magnitude of charge of the electron or proton is a natural unit of
charge.In any charging process, charge is not created ordestroyed:
it is merely transferred from one body toanother.The electric
charge is quantized. (1, 2, 3, 4)
- 5. 1.2 Conductors and Insulators Materials that allow easy
passage of charge are called conductors. Materials that resist
electronic flow are called insulators. The motion of electrons
through conducts and about insulators allows us to observe opposite
charges attract and like charges repel.Charging by induction
- 6. 1.3 Coulombs LawCharles Augustin de Coulomb (1736-1806)
studied theinteraction forces of charged particles in detail in
1784.
- 7. Point chargesCoulomb found that i) The electric force is
proportional to ii) The electric force between two point charges
depends on the quantity of charge on each body, which we will
denote by q or Q. ( positive or negative) + + - - + - - + r iii)
The forces that two point charges and exert on each other are
proportional to each charge and therefore are proportional to the
product of the two charges
- 8. Coulombs law state that;The magnitude of the electric force
between two pointcharges is directly proportional to the product of
thecharges and inversely proportional to the square of thedistance
between them.In mathematical term, the magnitude F of the force
thateach of two point charge and a distance r apartexerts on the
other can be expressed as; where k is a constant.1.3.1 Electric
Constants, kIn SI units the constant, k is where ( - epsilon nought
or opsilon zero) By approximation
- 9. Magnitude of the charge of an electron or proton, e One
Coulomb represents the negative of the total charge of about
electron.So that, the electric force is given as Superposition of
Forces: holds for any number ofcharges. We can apply Coulombs law
to any collection ofcharges.
- 10. ExampleTwo point charges and , areseparated by a distance
of 3.0 cm. Find the magnitudeand direction of (i) the electric
force that exerts on , and (ii) the electric force that exerts on
.Solution a) This problem asks for the electric forces that two
charges exert on each other, so we will need to use Coulombs law.
After we convert charge to coulombs and distance to meters, the
magnitude of force that exerts on is
- 11. Since the two charges have opposite signs, the force
isattractive; that is the force that acts on is directedtoward
along the line joining the two charges. b) Newtons third law
applies to the electric force. Even though the charges have
different magnitude, the magnitude of the force that exerts on is
the same the magnitude of the force that exerts on . So that
ExampleTwo point charges are located on the positive x-axis of
acoordinate system. Charge q1 = 1.0 nC is 2.0 cm from theorigin,
and charge q2 = -3.0 nC is 4.0 cm from the origin.What is the total
force exerted by these two charges on acharge q3 = 5.0 nC located
at the origin?SolutionFind the magnitude of
- 12. *(this force has a negative x-component because q3
isrepelled by q1)Then Find the magnitude of *(this force has a
positive x-component because q3 isattracted by q2)So the sum of
x-component is There are no y or z- components. Thus the total
force on q3 isdirected to the left, with magnitude .
- 13. 1.4 Electric FieldsWe defined the electric field at point
as the electricforce experienced by a test charge q0 at the
point,divided by the charge q0. The direction of and is the
same.
- 14. Electric field of a point charge Consider we have a charge
q as a point source. If we place a small test charge q0 at the
field point, P at a distance r from the point source, the magnitude
F0 of the force is given by Coulombs law so that, the magnitude of
electric field, E is But the direction of and is the same. Then
theelectric field vector is given as, is a vector unit in r
direction.
- 15. Example 1: Electric-field magnitude for a point chargeWhat
is the magnitude of electric field at a field point 2.0m from a
point charge q = 4.0 nC ?SolutionWe are given the magnitude of
charge and the distance from the object to the field point, so by
using we could calculate the magnitude of
- 16. Example 2: Electric Field Vector for a point charge.A point
charge q = -8.0 nC is located at the origin. Findthe electric-field
vector at the field point x = 1.2 m,y = -1.6 m?SolutionThe vector
of field point P isThe distance from the charge at point source, S
to thefield point, P is The vector unit,
- 17. Hence the electric-field vector is Example 3: Electron in a
uniform fieldWhen the terminals of a battery are connected to
twolarge parallel conducting plates, the resulting charges on the
plate cause an electric field in the region betweenthe plates that
is very uniform.If the plate are horizontal and separated by 1.0 cm
andthe plate are connected to 100 V battery, the magnitudeof the
field is E = 1.00 x 104 N/C. Suppose the isvertically upward,
- 18. a) If an electron released from rest at the upper plate,
what is its acceleration? b) What speed does the electron acquire
while traveling 1.0 cm to lower plate? Given electron charge is and
mass Solution: a) Noted that is upward but is downward because the
charge of electron is negative. Thus Fy is negative. Because Fy is
constant, the electron moves with constant acceleration ay given
by, b) The electron starts from rest, so its motion is in the y
direction only. We can find the electrons speed at any position
using constant-acceleration formula . We have and y0 = 0 so speed
when y = -1.0 cm.
- 19. Example 4: An electron trajectoryIf we launch an electron
into the electric field of Example3 with an initial horizontal
velocity v0, what is theequation of its trajectory?SolutionThe
acceleration is constant and in the y-direction. Hencewe can use
the kinematic equation for 2-dimensionalmotion with constant
acceleration. and We have ax=0 and ay = (-e)E /m . at t =0 , x0
=y0=0, v0x = v0and v0y=0, hence at time t, and Eliminating t
between these equations, we get
- 20. 1.5 Electric Fields CalculationIn real situations, we
encounter charge that is distributedover space. To find the field
caused by a distribution, weimagine the distribution to be made up
of many pointcharges, q1,q2,q3.qn. At any given point P, each
pointcharge produces its own electric field ,so a test charge q0
placed at P experiences a force from charge q1 and a force from
charge q2 and soon.From the principle of superposition of forces,
the totalforces that the charge distribution exerts on the q0 is
thevector sum of these individual forces, Then the total electric
field at point P,
- 21. Example 1:Point charge q1 and q2 of +12nC and -12nC
respectively,are placed 0.10 m apart. This combination of two
chargeswith equal magnitude and opposite sign is called anelectric
dipole. Compute the electric field caused by q1,the field caused by
q2, and total field (a) point a, (b) atpoint b, and (c) at point
c.Solution a) At point a: the electric field, caused by the
positive charge q1 and the field caused by the negative charge q2
are both directed toward the right. The magnitude of and are;
- 22. The component of and are; and and Hence at point a the
total electric field has components. At point a the total field has
magnitude 9.8 and is directed toward the right. b) At point a: the
electric field, caused by the positive charge q1 is directed toward
left and the field caused by q2 is directed toward the right. The
magnitude of and are;
- 23. The component of and are and and Hence at point a the total
electric field has components At point b the total field has
magnitude 6.2 and is directed toward the right. c) At point c, both
and have same magnitude, since this point is equidistant from both
charges and charge magnitude are the same;
- 24. The direction of and are shown in Figure. The x-component
of the both vector as the same From symmetry the y-component are
equal and opposite direction so add to zero. So at point c the
total electric field has magnitude and its direction toward the
right. 1.6 Electric Field LinesElectric field lines can be a big
help for visualizing electricfields and making them seem more real.
An electric fieldline is an imaginary line or curve drawn through a
regionof space so that its tangent at any point is in thedirection
of the electric field vector at that point.
- 25. Figure below shows some of the electric field lines in
aplane (a) a single positive charge, (b) two equal-magnitude
charges, one positive and one negative(dipole), (c) two equal
positive charges.Diagram called Field Map.