Electric field 2013
1.1 Electric Charge:
When a body is rubbed with a different body, a electric charge is produced. The quantity of
charge produced depends upon the nature of body. There are two different types of charges. The
charge produced by rubbing glass rod with silk is called as positive charge. The charge produced
by rubbing rubber (ebonite) rod with fur is negative charge.
1.2 Conductive of substance:
The capacity to conduct the electricity of a substance depends upon the number of free electrons.
There are three types of substances.
i) Conductors: The free electrons and their movement is not affected by the presence of atom of a
substance is called conductors.
Example: All metals like copper, gold, silver...
ii) Insulators: The electrons are tightly bound with atoms and are not free to move in substance
is called insulators.
Example: Wood, Plastic, Mica, Rubber,...
iii) Semiconductors: The same substance behaves like both conductors and insulating property
depends of temperature is called semiconductors.
Example: Silicon, Germanium, Gallium,...
1.3 COULOMB’S LAW
On the basis of experimental measurements of the force between the charges, Coloumb’s derived
two laws known as Coloumb’s laws of electrostatics.
I. First Law:
Like charges repell each other and unlike charges attract each other.
II. Second law:
The force exerted between two charges varies directly proportional to the magnitute of their
strength and inversely proportional to the square of the separation distance.
Proof of Coulomb’s law
Let consider q1and q2 are two charges separated at a distance r from each other. The electrostatic
force F can be calculated as fallow:
From second law,
Force, i) 𝐅𝛂 𝐪𝟏 . 𝐪𝟐
Dr.D.Baba Basha
q1
q2
r
...1
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Electric field 2013
ii) 𝐅𝛂
𝟏
𝐫𝟐
....2
Combine equation 1 and 2 gives
𝐪𝟏 . 𝐪𝟐
𝐅𝛂
𝐫𝟐
𝐪𝟏 . 𝐪𝟐
𝐅=𝐤
𝐫𝟐
Where k is called proportionality constant depends on the nature of medium.
The value of the constant:
The value of the constant k has been found experimentally as follows.
𝐊=
𝟏
𝟒𝝅𝜺𝟎
Where the constant 𝜺𝟎 (epsilon) is known as the permittivity of free space and has the value
8.854x 10-12 C2/Nm2.
𝐪𝟏 . 𝐪𝟐
𝐅=𝐤
𝐫𝟐
𝐊 = 𝟗𝐗𝟏𝟎𝟗 Nm2/C2
Vector form of Coulomb’s law
When dealing with Coulomb’s law, you must remember that force is a vector quantity and must
be treated accordingly. The law expressed in vector form for the electric force exerted by a charge
q1 on a second charge q2, written F12, is
𝐅𝟏𝟐 = 𝐤
𝐪 𝟏 . 𝐪𝟐
𝒓̂
𝐫𝟐
Where 𝒓̂ is a unit vector directed from q1 toward q2, as shown in figure. Because 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; that is, F21 = -F12.
Examples:
1. Two equal similar charges 3 cm apart in air repel each other with force 14.7 N. find the charge
in coulomb.
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Electric field 2013
2. The electron and proton of a hydrogen atom are separated (on the average) by a distance of
approximately 5.3 x10-11 m. Find the magnitudes of the electric force and the gravitational force between
the two particles.
3. A charge of +60 nC is 84 cm from a charge of -80 nC. What force will these charges exert on
a charge of +21 µC placed half way between them?
1.4 Electric Field:
According to Coulomb’s law a charged body placed near a charge, it experience a force, the field
or region in which the body place is called electric field.
An electric field is said to exist in the region of space around a charged object of the source
charge, when another charged object enters, an electric force act on it.
Or
The electric field can be defined as the region of the space in which a charged body experiences a
force.
Example: 1. A charge of 3µC is used to test the electric field of a central charge of 6C that causes
a force of 800N. What is the magnitude of the electric field?
Answer: 2.7 x108 N/C
1.5 Electric field line (Electric line of force)
If we place a small positive charge in an electric field it experience a force in a fixed direction, in
case if the charged body is like to free to move it will start moving in the direction of force. An
electric line of force is a path along which a unit positive charge would tend to move when free to
do so in an electric field.
Definition: Electric line of force is an imaginary line in the electric field, along which a unit
positive charge would tend to move freely to do so.
The line of forces for a positive and negative isolated charge is shown in the figures. In positive
charge, lines of force move away and vice versa in negative charge.
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Electric field 2013
The lines of force for equal and opposite charges and equal and similar charges are separated by a
distance are shown in the below figures.
Properties of Electric line of force:

They originate from positive charge and terminate on a negative charge.

Two lines of force proceeding in the same direction will repels and opposite direction, attract
each other.

Lines that indicate the strength and direction of the electric field.

The more dense the lines, the stronger the electric field.

Electric field is a vector quantity and its direction is tangent to the curve.
1.6 Conductors and Electric Fields (under electrostatic conditions)
2
The electric field is zero inside a charged conductor.
3
Excess charge on an isolated conductor resides on the surface.
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Electric field 2013
4
Excess charge accumulates on sharp points.
5
Electric field lines meet the conductor perpendicular to the surface of the conductor.
QUIZ:
1. Where are you safe during a thunderstorm?
A. In a car
or
B. Outdoors
2. Why can you not get radio reception in a tunnel or in a steel bridge?
3. Which field is stronger?
1.7 Electric Field for a Point Charge:
Let consider a test charge q0 is placed near a central charge q. The charge q0 is experience a
force due to charge q.
Electric Field is obtained in a similar way:
The force F can be expressed in Coulomb’s law as
𝐅=𝐤
𝐪 . 𝐪𝟎
𝐫𝟐
Therefore F= q0 E, where is vector E is the electric field caused by q0. The direction of the E
field is determined by the direction of the F, or the E field lines are directed away from positive q
and towards -q. The Force F on a charge q0 in an E field is
E=
𝐅
𝐪𝟎
, the SI unit is Newton/Coulomb (N/C)
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Electric field 2013
Since, the force, 𝐅 = 𝐤
E=
𝐤𝐪
𝐫𝟐
=
𝐪
𝟒𝝅𝜺𝟎 𝐫 𝟐
𝐪 .𝐪𝟎
𝐫𝟐
, then the electric field E is given by
, for air.
For more number of such charges, the net total electric field, E= E1+ E2+ E3+ ….
Example: 2. A test charge of +3µC is located 5m to the east of a -4µC charge.
A) Find the electric force felt by the test charge.
B) Find the electric field at that location. Answer: 4.32x10-3 N, 1.44 x 103 N/C along the –x axis.
Example: 3. If a test charge is moved to a location three times as far as its original location, how
does the electric field change?
Example: 4. Calculate the electric field felt by a test charge located half way between a charge of
+1C and a charge of -3C, that are 2m apart.
Answer: 1.8 x 1010 N/C
Example: 5. two equal positive charges, each of 2 µC interact with a third positive charge of 4 µC
situated is as shown in the figure. Calculate the magnitude and direction of the force on the 4 µC charge.
[The force bet. Q1 and Q is F= kQ1Q/r2 = 9x109x 2x10-6 x 4x10-6 / 0.52 = 0.288 N
The force bet. Q2 and Q is F= kQ1Q/r2 = 9x109x 2x10-6 x 4x10-6 / 0.52 = 0.288 N
The force Q resolve in to two components, along x axis is Fcosα and along y axis Fsinα (it cancel each
other, Fsinα=0 )
There the force on Q3 = 2Fcosα
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Electric field 2013
Q3 = 2x 0.288x 4/5
(cosα = adjesent/hypotenuse)
Q3 = 0.4608 N along x axis]
Example: 6. Calculate force on an electron in a uniform electric field of 5Χ 10 4 N / C due
north.
Answer: F = -8 Χ 10 -15 N
Example: 7. A water particle of mass 10 mg and having a charge of 1.5x10-6 C stays suspended in
a room. What is the magnitude of electric field in the room? What is its direction?
(Force, F = q E =mg)
Answer : E=65.3 N/C
Example: 8. Calculate the electric field felt by a test charge located half way between a
charge of +1C and a charge of -3C, that are 2m apart.
Dr.D.Baba Basha
Answer: 1.8 x 1010 N/C
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