Welcome
Physics E &M
Ms. Anu Elizabath Jose,
Physics teacher, Zayed educational complex, Al Dhait.
Physics electricity and
magnetism
UNIT 2 ELECTRIC
GAUSS LAW
FIELD
AND
Electric field lines
LO: Using the definition of electric field,
calculate
unknown
quantities
INTRO
(such
as
charge, force, field, and direction of field)
key concepts
electric field , field lines, test charge
Gauss theorem
Electric field
Electric charge
properties
Electric flux
Charged distributions
Ch02 – Electric Fields and
Gauss’s Law
5. Sketch the trajectory of a known charged
particle placed in a known uniform electric
field.
1. Using the definition of electric field, unknown
quantities (such as charge, force, field, and
direction of field) can be calculated in an
electrostatic system of a point charge or an object
with a charge in a specified electric field.
2. Describe and calculate the electric field due to
a single point charge, a dipole or a configuration of
two or more static-point charges.
3. sketch, Explain or interpret an electric field
diagram of a system of charges.
4. Determine the qualitative nature of the motion
of a charged particle of specified charge and mass
placed in a uniform electric field.
6. Determine the motion of a charged object
of specified charge and mass under the
influence of an electrostatic force.
7. Derive expressions for the electric field of
specified charge distributions using integration
and the principle of superposition
8. Describe an electric field as a function of
distance for the different types of
symmetrical charge distributions
9. State and apply the general definition of
electric flux.
● . An electric field, E(r), is defined at any point in space,
as the net electric force on a charge, divided by that
charge:
● 𝑬=
𝑭𝑬
𝒒
=
𝒌𝑸
𝒓𝟐
=
𝟏 𝑸
𝟒𝝅𝜺𝒐 𝒓𝟐
● The units of the electric field are newtons per
coulomb (N/C).
● The electric force on a charge at a point is parallel or
antiparallel, depending on the sign of the charge in
question) to the electric field at that point and
proportional to the magnitude of the charge.
● The direction of the force on a positive charge is
along the direction of E and the force on a negative
charge is in the direction opposite to E
Electric field
Superposition principle
●
if several sources of electric
fields are present at the same
time, such as several point
charges, the electric field at
any given point is determined by
the superposition of the electric
fields from all sources.
●
𝑬𝒏𝒆𝒕 = 𝑬𝟏 + 𝑬𝟐 + 𝑬𝟑 + 𝑬𝟒 + ⋯
Electric field lines
The changing direction and strength of the electric field can be visualized by means
of electric field lines.
The direction of the field line at each point is the same as the direction of the force
at that point, and the density of field lines is proportional to the magnitude of the
force.
Electric field lines point away from sources of positive charge and toward sources of
negative charge. An electric field is a vector quantity, and thus the components of
the field must be added separately
Concept check 1
General Observations
1. Field lines originate at positive
charges and terminate at negative
charges.
2. Field lines never cross
Concept check 2
Concept check
2.11 What are the signs of the charges in the
configuration shown in the figure?
a) Charges 1, 2, and 3 are negative.
b) Charges 1, 2, and 3 are positive.
c) Charges 1 and 3 are positive, and 2 is
negative.
d) Charges 1 and 3 are negative, and 2 is
positive.
e) All that can be said is that the charges have
the same sign
Classwork 1:
A point charge, q = 6n C, is placed on the x-axis at the
origin. What is the electric field produced at x = 12 cm?
Classwork 2- two charges
A +2 nC point charge is placed at one corner of a square
(1.00 m on a side), and a -3 nC charge is placed on the
corner diagonally opposite. What is the magnitude of the
electric field at the corner, P?
P
Classwork 2- two charges
A +2 nC point charge is placed at one corner of a square
(1.00 m on a side), and a -3 nC charge is placed on the next
corner. What is the magnitude of the electric field at the
corner, P?
P
Classwork -Three Charges
• Figure shows three fixed point charges: q1
= +1.50 µC, q2 = +2.50 µC, and q3 = 3.50 µC. Charge q1 is located at (0,6), q2
is located at (0,0), and q3 is located at
(8,0). What electric field, do these three
charges produce at the point P = (b,a)?
Classwork
Figure shows three fixed point charges: q1
= +1.50 µC, q2 = +2.50 µC, and q3 = -3.50
µC. Charge q1 is located at (0,a), q2 is
located at (0,0), and q3 is located at (b,0),
where a = 8.00 m and b = 6.00 m. What
electric field, do these three charges
produce at the point P = (b,a)?
Electric field due to dipole
● A system of two equal (in magnitude) but
oppositely charged point particles is called
an electric dipole. The electric field from an
electric dipole is given by the vector sum of
the electric fields from the two charges
Exit ticket
Each apple contains equal
numbers of positive and
negative charges, so they
appear neutral to each
other
● An apple contains trillions of charged
particles. Why don’t two apples repel
each other when they are brought
together?
The electric field passing through a
given area A is called the electric
flux and is given by,
𝝓 = 𝑬. 𝑨 𝒄𝒐𝒔𝜽
In simple terms, the electric flux is
proportional to the number of electric
field lines passing through the area.
In a closed-surface case, the total,
or net, electric flux is given by an
integral of the electric field over the
closed surface,
𝝓=
𝑬. 𝑨 𝒄𝒐𝒔𝜽
Electric flux
Gauss theorem
● the net charge inside a closed
surface, called the Gaussian
surface,
● 𝝓=
𝒒
𝝐𝟎
=
𝑬. 𝑨 𝒄𝒐𝒔𝜽
● Gauss’s Law states that the surface
integral of the electric field
components perpendicular to the
area times the area is proportional to
the net charge within the closed
surface
Two important consequences of Gauss’s
Law are evident:
1. The electrostatic field inside any
isolated conductor is always zero.
2. Cavities inside conductors are
shielded from electric fields
Electric charge distribution
Electrostatic
shielding
● any cavity inside a
conductor is totally shielded
from any external electric
field. This effect is
sometimes called
electrostatic shielding
Charge distributions
During charge transfer the charges in spheres redistribute, spreading out evenly.
Charge
● An electroscope is a scientific device that is used
transfer
to detect the presence of an electric charge on a
body.
● The electroscope below consists of a plate (near
the top), a support stand (which connects to the
plate and extends through the center of the scope),
and a needle which rests upon the support stand
and is free to rotate about its pivot.
● The plate, support stand, and needle are all made of
a conducting material which allows for both the
free flow of electrons and the distribution of any
excess charge throughout the electroscope. By
observing any deflection of the needle, the
presence of charge in either the electroscope or a
nearby object can be determined
Example
When a positively charged rod is brought
near, but does not touch, the initially neutral
electroscope shown above, the leaves repel
(I). When the electroscope is then touched
with a finger, the leaves hang vertically (II).
Next when the finger and finally the rod are
removed, the leaves repel again (III). During
the process shown in Figure II
A. electrons are going from the electroscope
into the finger
B. electrons are going from the finger into
the electroscope
C. protons are going from the rod into the
finger
D. protons are going from the finger into the
rod
E. electrons are going from the finger into
the rod.
Example
Concept check
Electrostatic Force
Main topic
Electrostatic force
LO:
Calculate the net electrostatic
force on a single point charge
due to other point charges, or
the distances between charges
in a system of static point
charges
Coulomb’s law
𝒌𝑸𝟏 𝑸𝟐
𝟏 𝑸𝟏 𝑸𝟐
𝑭𝑬 =
=
𝟐
𝒓
𝟒𝝅𝜺𝒐 𝒓𝟐
starter
Coulomb’s law
●
Coulomb’s Law finds out
the magnitude of the
electrostatic force
between the charges. The
unit of the electrostatic
force is Newton (N)
Concept check 2
Three small spheres, A, B, and C, have charges
with magnitudes qA, qB, qC , respectively. The
three spheres are aligned along a straight
line, as shown in the figure above. At the
instant shown, the net force on sphere A is
zero.
1) The ratio of qC/qB is
a) 4/9
b) 9/4
c) ½
d) 3/2
e) 2/3
Concept check 3
Three small spheres, A, B, and C, have charges
with magnitudes qA, qB, qC , respectively. The
three spheres are aligned along a straight
line, as shown in the figure above. At the
instant shown, the net force on sphere A is
zero.
2. Which of the following statements
must be true of the signs of the charges?
(A) Only charges q a and q B have the
same sign.
(B) Only charges q a and qC have the
same sign.
(C) Only charges q B and q C have the
same sign.
(D) Charges q B and qC have different
signs.
(E) Charges qA, qB and qC all have the
same sign.
Starter
Coulomb’s law
review
● Electrostatic force between
two charges is given by,
●
𝒌𝑸𝟏 𝑸𝟐
𝟏 𝑸𝟏 𝑸𝟐
𝑭𝑬 =
=
𝟐
𝒓
𝟒𝝅𝜺𝒐 𝒓𝟐
If charge 2 exerts the force,
𝑭𝟐→𝟏 on charge 1, then the
force that charge 1 exerts on
charge 2, 𝑭𝟏→𝟐 is simply
obtained from Newton’s Third
Law: 𝑭𝟏→𝟐 = −𝑭𝟐→𝟏
Superposition principle
● The principle of superposition
states that when a number of
charges are interacting, the net
electrostatic force a given
charge is the vector sum of the
forces exerted on it due to all
other charges. The force
between two charges is not
affected by the presence of
other charges.
𝑭𝒏𝒆𝒕 = 𝑭𝟏 + 𝑭𝟐 + 𝑭𝟑 +…
Charges in
equilibrium
● Use Coulomb’s Law to find a
location where a third charge
can be placed to experience zero
force.
Equilibrium
condition
● If an object is at
●
equilibrium, then the
forces are balanced.
Find an equilibrium point (a
point where the forces sum
to zero is at equilibrium,
using Coulomb’s law.
●
●
●
●
●
●
Steps
Sketch the problem
Label the charges, with
signs.
find the possible
location where the net
force is zero.
Choose the distance of
the point charge,
whose net force is
zero, as ‘x’.
Equate the equations of
Example
Two charged particles are placed as shown in q1 = 0.15 µC is
located at the origin, and q2 = 0.35 µC is located on the
positive x-axis at x2 = 0.40 m. Where should a third charged
particle, q3, be placed to be at an equilibrium point (such that
the forces on it sum to zero)?
Concept check
a)
b)
●
1.68 Two charged objects
experience a mutual
repulsive force of F N. If the
charge of one of the objects
is reduced by half and the
distance separating the
objects is doubled, what is
the new force?
c)
d)
F/2
F/4
F/8
2F
Starter- AP
Two particles, each of charge
+Q, are fixed at opposite corners
of a square that lies in the plane
of the page. A positive test
charge +q is placed at a third
corner. If F is the magnitude of
the force on the test charge due
to only one of the other charges,
what is the magnitude of the net
force acting on the test charge
due to both of these charges?
Starter- AP
Two particles, each of charge +Q, are
fixed at opposite corners of a square
that lies in the plane of the page. A
positive test charge +q is placed at a
third corner. What is the magnitude of
the force on the test charge due to the
two other charges?
a) F
𝟐F
b) 2F C)
𝑭
𝟐
d) 3
𝑭
𝟐
e)
Gravitational law and coulomb’s law
●
Gravitational law is the
force of attraction between
two masses , given by,
𝑭𝑮 =
𝑮𝒎𝟏 𝒎𝟐
𝒓𝟐
= 𝒎𝒈
Where the gravitational field
𝒈=
𝑮𝒎
𝒓𝟐
●
Coulomb’s law is the electrostatic
force between two charged
particles, given by,
𝑭𝑬 =
𝒌𝑸𝟏 𝑸𝟐
𝒓𝟐
= 𝑬𝒒
And the electric field, 𝑬 =
𝒌𝒒
𝒓𝟐
Charged pendulum
● Consider two charges hanging from a
common point by two strings. They are
both charged with charge q and both
have mass m. They dangle under the
influence of both electrostatic forces
and gravitational force.
● From the FBD
𝒌𝑸𝟏 𝑸𝟐
𝑻𝒄𝒐𝒔 𝜽 = 𝑭𝒆 =
𝒓𝟐
𝑻𝒔𝒊𝒏 𝜽 = 𝑭𝒈 = 𝒎𝒈
𝒕𝒂𝒏 𝜽 = 𝑭𝒈 /𝑭𝒆
Classwork
Two identical charged balls hang
from the ceiling by insulated ropes
of equal length, ℓ = 1.50 m). A
charge q = 25.0 µC is applied to
each ball. Then the two balls hang
at rest, and each supporting rope
has an angle of 25.0° with respect
to the vertical . What is the mass of
the ball if tension is 4N?.
Example
●
A 10.0 g mass is suspended
5.00 cm above a
nonconducting flat plate,
directly above an embedded
charge of q (in coulombs). If
the mass has the same
charge, q, how much must q
be so that the mass levitates
(just floats, neither rising
nor falling)?