General physics II (22102)
Dr. Iyad SAADEDDIN
Chapter 21: Electric Charge
In this chapter we will cover
„ Properties of Electric Charges
„ Conductors and insulators
„ Coulomb’s Law
21-1 What is physics?
„
Many devices depend on the physics of electromagnetism
(combination of electric and magnetic phenomena). This physics is
the root of computers, television, radio, telecommunications, house
lighting, etc ……
„
the sciences of electricity and magnetism developed separately for
centuries—until 1820, before exploring the connection between them
(physics of Electromagnetism)
„
Phenomena of electric force discovered
in ancient Greek times (700 BC). who discovered
that if a piece of amber (‫ )آﻬﺮﻣﺎن‬is rubbed and
then brought near bits of straw (‫)ﻗﺶ‬, the straw
will jump to the amber due to this electric force
„
Presence of electric force is due to the
presence of what is called Electric Charge
21-2, 5, 6: Properties of electric charge
„
Electric charge is an intrinsic property of fundamental
particles (atoms) making up the materials.
„
types of charges:
„
Charged object
„
Positive charge (+ve)
21-2, 5, 6: Properties of electric charge
Consider a positively charged glass rod suspended by a thread
„ Negative charge (-ve)
„
When +ve and –ve charges are equal within object Æ electrically
neutral object.
„
If object charge is not balanced Æ charged object
„
examples: whenever two non-conducting substances are
rubbed together
* Hard rubber rubbed with fur Æ rubber of negative charge (-ve)
* Glass rod rubbed with silk Æ glass of positive charge (+ve)
„
Electrostatic phenomena in dry
weather; pieces of papers stick to
together and to the plastic comb,
The charge manifest it self by attraction or repulsion of
charged materials
a) It is attracted to a -ve
charged plastic rod.
(b) It is repelled by another
+ve charged glass rod.
Two types of charges named by Benjamin Franklin
(1706-1790) as positive and negative
Æ Like charges repel and Unlike charges attract
Dr. Iyad
SAADEDDIN
General physics II (22102)
21-2, 5, 6: Properties of electric charge
„
Electric charge is not created; Usually, negative
charge is transferred from one object to the other.
Î Electric charge is always conserved
When a glass rod is rubbed with silk,
electrons are transferred from the glass to
the silk.
Æ Silk will have –ve charge and glass will
have equal amount of +ve charge
21-2, 5, 6: Properties of electric charge
What Carries Charge?
Electric charge come from the particles making up the
basic unit of matter (the atom)
„ Atoms consist of:
„
„
+ve charge is that carried by protons
„
-ve charge is that carried by electrons
„
electrically neutral neutrons In atom.
The protons and neutrons are packed tightly
„
Grounding
: The “Earth” is
together in a central nucleus.
considered an infinite sink of charges
21-2, 5, 6: Properties of electric charge
„ Robert Millikan found, in 1909, that all charges are integer multiple of
an elementary charge e
ÎCharge is quantized Î Any charged object must have a charge of
±e, or ± 2e, or ± 3e, etc., but not say ± 1.5e.
Î q = ± ne (n =1, 2, 3, … is an integer)
A neutral atom has
positive charges = negative charges.
„ The value of elementary charge e is
|e| = 1.60219 x 10-19 C.
Unit: In SI unit system , electrical charge
is measured in coulomb (C). The coulomb unit is derived from the SI
unit ampere for electric current i
„
21-2, 5, 6: Properties of electric charge
(summary)
„
Charge is carried by electrons and protons.
„
Can be positive or negative.
„
Like charges repel, opposite charges attract.
„
Total charge in a system is conserved.
„
Charges come in discrete quantities (quantized).
„
Charges are measured in Coulombs (C).
„
Usually denoted by q.
Dr. Iyad
SAADEDDIN
General physics II (22102)
21.3 conductors and insulators
21.4 Coulomb's Law
All materials are full of +ve and –ve charges (electrons and
protons). In term of conductivity, we have 4 types of materials
„
Electrical Conductivity
Nonconductors
or Insulators
Semi-conductors
No movement of
charges within the Limited number of free
object (only very
carriers (intermediate
few can move). between conductors and
Like rubber,
insulators).
plastics and
Like Silicon and
glass
Germanium
„
perfect conductors,
allowing charge to
move without any
difficulty.
Charges move
freely.
Like Metals
(Cu, Ag, Al)
(HgBa2Ca2Cu3O8+δ)
The properties of conductors and insulators are due to the
structure and electrical nature of atoms.
„
Coulombs law: when two charges brought together and separated
by a distance r, there exist an electric force between these charges
„
superconductors
Conductors
Dr. Iyad
SAADEDDIN
„
Charles Coulomb discovered in 1785 the
fundamental law of electrical force between two
stationary charged particles using torsion balance.
An electric force has the following properties:
„ Inversely proportional to the square of the
separation, r, between the particles, and is
along a line joining them.
„ Proportional to the product of the magnitudes
of the charges |q1| and |q2| on the two particles.
„ Attractive if the charges are of opposite sign
and repulsive if the charges have the same
sign.
„ It is conservative force
21.4 Coulomb's Law
Torsion
balance
21.4 Coulomb's Law
Mathematical formulation for
coulomb’s law is Æ electrostatic
force has a magnitude of
„
q1
r
q2
Fe = F = k
ke = k =
q1 q2
r2
(N = Newton)
1
= 8.99 × 109 N.m 2 C 2
4πε 0
ε 0 = 8.85 × 10 −12 C 2 N.m 2
ε 0 is permitivity of free space
r
r
F12 = − F21
Electrostatic force is a
force has a magnitude
and direction
„
Charges have same
sign Î repulsive force
Charges have different
sign Î attractive force
r
qq
F12 = k 1 2 2 rˆ
r
General physics II (22102)
21.4 Coulomb's Law
mm
Coulomb’s law like Newton’s law of gravity Fg = G 1 2 2
r
ƒ Both are Field forces (no direct contact between charges)
1
ƒ both are inverse-square laws (Fα 2 )
r
ƒ But Fe >> Fg between charged particles Î Fg can be neglected
ƒEx: in hydrogen atom, the forces ration between an the electron
and the proton separated by 5.3x10-11 m is (Fe/Fg ≈ 2×1039)
21.4 Coulomb's Law
„ If there are more than two charged particles in a system,
then we can calculate the force on a particle by making vector
summation for the force of all other particles on that one
(super position principle).
For example if we have N charged particles, then the force on
particle 1 is
N r
r r
r
r
r
F1 = F21 + F31 + ..... + FN 1 = ∑ Fi1 = Fnet ,1
Charge and Mass of the Electron, Proton and Neutron.
Particle
Charge ( C)
Mass (kg)
Electron
-1.60 ×10+19
9.11 × 10+31
Proton
+1.60 × 10+19
1.67 × 10+27
Neutron
0
1.67 × 10+27
i =2
N r
N r
N r
r
F1 = ∑ Fi1iˆ + ∑ Fi1 ˆj + ∑ Fi1kˆ
i=2
21.4 Coulomb's Law: Shell theorem
Shell theorems for spherical
symmetry:
„
1- A spherical shell of
uniform charge Q attracts or
repels a charged particle q
that is outside the shell as if
all the shell’s charge were
concentrated at its center.
2- If a charged particle q is
located inside the spherical
shell of uniform charge Q,
there is no net electrostatic
force on the particle from the
shell.
i =2
21.4 Coulomb's Law: Spherical conductor
For a spherical conductor, If excess
charge is placed on that conductor, the
excess charge spreads uniformly over
the (external) surface; charges repel one
another and tend to move apart Æ
charges spread over the available
surface until they are uniformly
distributed
„
„
„
i =2
FQq = k
Qq
r2
Q is uniformly distributed on the
surface of the conductors forming
spherical shell of charges
FQq = 0
That arrangement maximizes the
distances between all pairs of the
excess distributed charges on spherical
surface forms a spherical shell of
uniform charge Æ we can apply shell
Q is uniformly distributed on the
theorem for spherical conductors
surface of the conductors forming
charges.
spherical shell of charges
„
Dr. Iyad
SAADEDDIN
General physics II (22102)
21.4 Coulomb's Law: Example – continued
from previous slide q1=1.6×10-19 C and q2=3.2×10-19
21.4 Coulomb's Law: Example
(a) two positively charged particles, q1=1.6×10-19 C and q2=3.2×10-19 C, lies
on x-axis with separation between them R = 0.02 m, what is the electrostatic
force magnitude and direction on particle 1 from particle 2?
The force magnitude from 2 on 1 is
(b) If a third charged particle (q3= - 3.2×10-19 C)
is placed between the first two particles at a
distance ¾ R from particle 1, find the net force
on particle 1.
Force of 3 on 1
(–ve x-axis)
Note: force from 1 on 2 will have same magnitude but in opposite direction
Æ The net force on particle 1 is
21.4 Coulomb's Law: Example – continued
from previous slide q1=1.6×10-19 C and q2=3.2×10-19
(b) If third particle is removed and a forth
particle is added (q4= - 3.2×10-19 C) and placed
at a distance ¾ R from particle 1 and at angle
60° with x-axis, find the net force on particle 1.
21.4 Coulomb's Law: Exampe
Ex:Three point charges lie along the x axis as shown. The positive charge q1
= 15 µC is at x=2 m, the positive charge q2 = 6 µC is at the origin, and the net
force acting on q3 is zero (q3 is at equilibrium). What is the x coordinate of q3?
Force of 4 on 1
Æ net force on particle 1 is
At x between the
two charges
Notes:1- equilibrium is always between similar charges,
2- equilibrium is not between different charges and near the small one
Dr. Iyad
SAADEDDIN
General physics II (22102)
21.4 Coulomb's Law: Example
21.4 Coulomb's Law: Example
Two conducting spheres A and B with charge initially shown (a) connected and
disconnected as show. Calculate charge and force after disconnection for each case
Electrons transfere
from B to A
reaching equilibrium
qB=0
A and B are
momentary
connected by
conducting wire
Ex: Consider three point charges located at the corners of a right
triangle as shown in where q1 = q3 5 µC, q2 = -2 µC, and a = 0.1 m.
Find the resultant force exerted on q3.
Both will
have + Q/2
charge
Charge on A will A momentary
distributed on A connected to
ground
and B
A will have
no charge
Æ
21.4 Coulomb's Law: Example – continued
from previous
r
F23 = F23 cos180°iˆ + F23 sin 180° ˆj
r
F23 = −9iˆ
21.4 Coulomb's Law: Example
Ex: Two identical small charged spheres, each having a mass of 3×10-2 kg,
hang in equilibrium as shown. The length of each string is 0.15 m, and the
angle θ is 5°. Find the magnitude of the charge on each sphere.
If we look at only
one sphere (left)
free body diagram
for left sphere is
r
F13 = F13 cos 45°iˆ + F23 sin 45° ˆj
r
= 7.9 iˆ + 7.9 ˆj
r
r
Hence, F3 = F13 + F23 = −1.1iˆ + 7.9 ˆj
Equilibrium Æ
acceleration = 0 m/s2.
apply Newton 2nd law
Dr. Iyad
SAADEDDIN
General physics II (22102)
21.4 Coulomb's Law: Example – continued
from previous slide
Summary
„
„
„
But
and r=2a
„
„
+ve or -ve
Charges can be negative or positive.
Charge is discrete, conserved.
Like charges repel, opposites attract.
Types of materials : Insulators,
Semiconductors, conductors
Electrostatic force obeys Coulomb’s Law.
Dr. Iyad
SAADEDDIN