Phys 2180 Lecture (1)
Electrical Charges and Coulomb’s Law
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Structure of Matter
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+ + -
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• Fundamental building blocks of the
matter are atoms.
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Structure of Matter
• Neutral atom – electron = Positive ion
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+ -
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+ +
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- -
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3
1electron charge  1.60210-19
C

Structure of Matter
• Neutral atom + electron = negative ion.
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+ + -
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Electrical Charges
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• Electrostatics is the study of electric charge at rest.
• Electric charge is a fundamental property of matter.
– Two types of electric charges
• Positive charge - every proton has a single positive charge.
• Negative charge - every electron has a single negative
charge.

Fundamental Charges
Note that the electron and proton both have the
same charge, with the electron being negative and
the proton being positive. This amount of charge is
often called the electronic charge, e. This
electronic charge is generally considered a positive
value (just like g in gravity). We add the negative
sign when we need to:
qe = -e; qp = +e.
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Fundamental Charges
7

•Electrostatics is the study of electric charge at rest.
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Electric charge
Two different kinds of charge, positive and negative.
Electricity, with attractive and repulsive forces, needs two kinds of charge.
• Electric charge is measured in coulombs (C)
Properties of electric charge
1.Two kinds of charges occur in nature,
o like charges repel one another,
o and unlike charges attract one another.
2. Charge is conserved.
3. Charge is quantized.
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• An object becomes electrostatically
charged by:
1. Friction,which transfers electrons
between two objects in contact,
1. Contact with a charged body which
results in the transfer of electrons,
2. Induction which produces a charge
redistribution of electrons in a material. 10

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Types Of Forces
• There are only four fundamental forces of nature.
• Gravitational Force
• Electromagnetic Force
• Strong Nuclear Force
• Weak Nuclear Force

Electric Field - Definition
Note that since F is a vector and q is a scalar,
E must be a vector.
the units of Electric Field in SI units of newtons per coulomb (N/C)
• the electric field vector E at a point in space is defined as the electric force
Fe acting on a positive test charge q placed at that point divided by the
test charge:
F = K|q||q|/r2 = magnitude of the electric force
k = Coulomb's constant = 8.9875 x 109Nm2/c2
E = K|q| / r2
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Electric Field Lines
• The electric field lines for a point charge.
• (a) For a positive point charge, the lines are directed radially outward.
• (b) For a negative point charge, the lines are directed radially inward.
• Or the electric field lines extend away from positive charge (where they
originate) and towards negative charge (where they terminate) 12

Electric Force: Coulomb’s Law
14

Electric Force: Coulomb’s Law
• we can express 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 the Coulomb constant, q1 and q2 the
charges, r is the distance between the charges.
We also found that the force decreases with distance between the
charges just like gravity.
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Electric Force: Coulomb’s Law
 The value of the Coulomb constant depends on the choice of units. The SI unit of charge is the
coulomb (C).
 The Coulomb constant ke in SI units has the value
where the constant epsilon is known as the permittivity of free space
ε0 ≅ (8.854 187 817)*10-12 C2/(N m2)
15
1 Coulomb = 106 microCoulomb
1 Coulomb = 109 nanoCoulomb

Problem (1)
• The average distance r between the electron and the proton in the hydrogen
atom is 5.3x10-11 m. (a) What is the magnitude of the average electrostatic
force that acts between these two particles? (b) What is the magnitude of
the average gravitational force that acts between these particles?
• Solution
• the electrostatic force,
• the gravitational force,
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𝑭𝒆 = 𝑲
𝒒𝟏𝒒𝟐
𝒓𝟐
=
(8.99 X 109N.m2/C2)(1.60X l0−19C)2
(5.3 X 10−11 m)2
= 8.2 X 10-8 N
𝑮
𝒎𝟏𝒎𝟐
𝑭 = 𝑮
𝒓𝟐
=
(6.67 X 10−11N.m2/kg2)(9.11X l0−31kgX1.67X l0−27kg)
(5.3 X 10−11 m)2
-57

• The nucleus of an iron atom has a radius of about 4x10-15 m and
contains 26 protons. What repulsive electrostatic force acts between two
protons in such a nucleus if a distance of one radius separates them?
• Solution
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Problem (2)
𝒆
𝒒𝟏𝒒𝟐
𝑭 = 𝑲
𝒓𝟐
=
(8.99 X 109N.m2/C2)(1.60X l0−19C)2
(4 X 10−15 m)2
= 14 N

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Problem (3)
Two balloons with charges of +3.37 µC and -8.21 µC attract each other with a force of
0.0626 N. Determine the separation distance between the two balloons.
Solution:
Given:
q1 = +3.37 µC = +3.37 x 10-6 C , k= 8.99 X 109N.m2/C2
q2 = -8.21 µC = -8.21 x 10-6 C
Fe = -0.0626 N (use a - force value since it is attractive)
Find: r = ???
𝑒
𝐹 = 𝐾
𝑞 𝑞
1 2
𝑟2
𝑟2 = 𝐾
𝑞1𝑞2
𝐹𝑒
𝑟2 = 𝐾
𝑞1𝑞2
𝐹𝑒
r = 𝐾
𝑞1𝑞2
𝐹𝑒
=
(8.99 x 109 Nm2/C2) (−8.21 x 10−6 C)(+3.37 x 10−6 C)
(−0.0626 N)
r = +3.98 m2
=1.99 m

Three Charges on a Line
Determine the magnitude and direction of the net force on q1.
Problem (4)

8.99109
Nm2
C2
3.0106
C 4.0106
C 
0.20m2
 2.7N
r2
q1 q2
F12  k 
8.99109
Nm2
C2
3.0106
C 7.0106
C 
0.15m2
 8.4N
r2
q1 q3
F13  k 
→ → →
F  F12  F13  2.7N8.4N  5.7N
Problem (4)

18.5 Coulomb’s Law
Find the net force on q1
F  F12 sin F13 cos

18.5 Coulomb’s Law
0.15m2
8.99109
N m2
C2
4.0106
C2
6.0106
C2
  9.59N
q1 q2
F12  k 
8.99109
N m2
C2
4.0106
C2
5.0106
C2

0.10m2
 17.98N
r2
r2
q1 q3
F13  k 
F  F12 sin F13 cos9.59sin 7317.98cos73 14.43N