Transcript Electrostatics - Effingham County Schools

Electrostatics: Coulomb’s Law & Electric Fields
Electric Charges

There are two kinds of charges:
positive (+) and negative (-), with the
following relationships:
 Like charges (same sign) repel each
other
 Unlike charges (opposite sign) attract
each other
Characteristics of Electric
Charge
Electric charge is never created or
destroyed – it is conserved
 Charge always comes in a multiple of a
basic unit: e-,

 where e = 1.602 x 10-19 Coulombs (C)
 The charge on an electron is -1.602 x 10-19
Coulombs
 A proton has the opposite charge
Electric Charges

Charge always comes in a multiple
of that basic unit:
 q = Ne,
 where q is charge and N is the number
of electrons or protons
Problem One:

A certain static discharge delivers
-0.5 Coulombs of electrical charge.
How many electrons are in this
discharge?
Sample Problem
A certain static discharge delivers -0.5 Coulombs of electrical charge.
How many electrons are in this discharge?
Problem Two

How much positive charge resides in
two moles of hydrogen gas? (H2)

How much negative charge?

How much net charge?
Sample Problem
1.
How much positive charge resides in two moles of
hydrogen gas (H2)?
2.
How much negative charge?
3.
How much net charge?
Transfer of Electric Charge

Charge can be transferred between
objects
 Transfer of charge is almost always due to the
transfer of electrons
 Remember: Atomic nuclei are fixed, but the
outer electrons are more easily separated,
leaving negative electrons and positive ions
Coulomb’s Law
Coulomb’s Law
When opposite charges (let’s say q1 and q2)
are separated, they are attracted by an
electric force (like charges are repelled)
 The attractive force can be determined using
Coulomb’s Law:


Where q1 and q2 are charges, k is the electrostatic
constant, and r is the distance between the charges
Electrostatic Constant

A quick note:
 k = 1/(4πε0)
 ε0 is the permittivity of free space
 ε0 = 8.85 x 10-12 C2/Nm2
 BUT
you don’t need to know that,
because you can use k = 9.0 x 109
Nm2/C2

By the way, Coulomb’s Law only applies directly to
spherically symmetric charges
Coulomb’s Law Example
The radius of a hydrogen atom is
5.29 x 10-11 m
 What is the electric force between a
proton and an electron in a
hydrogen atom?


A hydrogen atom has one proton in its
nucleus and one electron orbiting the
nucleus. The magnitude of the charge of
the electron is the same as the
magnitude of the charge of the proton
and equals 1.60 × 10−19 C. The
magnitude of the electric force is
determined by the Coulomb’s Law
Yet Another Problem

A point charge of positive 12.0 C
experiences an attractive force of 51
mN when it is placed 15 cm from
another point charge. What is the
other charge?
Sample Problem
A point charge of positive 12.0 μC experiences an attractive force of 51 mN
when it is placed 15 cm from another point charge. What is the other
charge?
Superposition
 Electric
force (like ALL forces) is a
vector quantity. (don’t you just love
geometry?)
 If a charge is subjected to forces from
more than one other charge, we use
VECTOR ADDITION! Yay!
 Sometimes that’s called superposition
(just so you know)
Practice with
Superpositon

What is the
force on
the 4 C
charge?
Sample Problem
• What is the force on the 4 C charge?
y (m)
2.0
1.0
-3 C
2 C
1.0
4 C
2.0x (m)
The Electric
Field
The presence of electric charge modifies
empty space. The electric force can act
on charged particles without actually
touching them (like gravity acts on distant
masses)
 We say that an “electric field” is created in
the space around a charged particle or a
configuration of charges

The Electric Field
If a charged particle is placed in an
electric field created by other charges, it
will experience a force from the field
 Sometimes we know about the electric
field without knowing about the charge
configuration that created it. We can
easily calculate the electric force from
the field instead of the charges.

Why use fields?





Forces exist only when two or more particles are
present
Fields can be calculated for just one particle
Fields exist even if there is no net force
The arrows in a field are
NOT VECTORS – they are
LINES OF FORCE
Field lines indicate the
direction of force on a
positive charge placed in
the field (opposite for
negatives)
Field between charged
plates
Calculating Electric Field
 The
force on a charged particle
placed in an electric field can
be calculated by:
 F = Eq
 F: Force (N)
 E: Electric Field (N/C)
 Q: charge (C)
Field Practice

The electric field in a given region is
4000 N/C pointed North. What is the
force exerted on a 400 g styrofoam
bead bearing 600 excess electrons
when placed in the field?
Sample Problem
The electric field in a given region is 4000 N/C pointed
toward the north. What is the force exerted on a 400 μg
styrofoam bead bearing 600 excess electrons when
placed in the field?
More Practice

A proton traveling at 440 m/s in the
+x direction enters an electric field of
magnitude 5400 N/C directed in the
+y direction. Find the acceleration.
Sample Problem
A proton traveling at 440 m/s in the +x direction enters an
an electric field of magnitude 5400 N/C directed in the
+y direction. Find the acceleration.
Spherical Electric Fields
The electric field surrounding a point
charge or spherical charge can be
calculated by:
 E = kq/r2

 E: Electric field (N/C)
 K: 9x109 Nm2/C2
 q: Charge (C)
 r: distance from center of charge q (m)
Superposition with Fields
When more than one charge
contributes to the electric field, the
resultant field is the vector sum of the
electric fields from the individual
charges
 Remember: Electric field lines are
NOT VECTORS, but can be used to
find the direction of the electric field
vectors.

Yay More Practice

A particle bearing -5.0 C is placed
at -2.0 cm, and a particle bearing
5.0  C is placed at 2.0 cm. What is
the field at the origin?
Sample Problem
A particle bearing -5.0 μC is placed at -2.0 cm, and a
particle bearing 5.0 μC is placed at 2.0 cm. What is the
field at the origin?
Electrostatics: Electric Potential & Potential Energy;
Energy Conservation & Potential
Equipotential Lines
Electric Potential Energy

Electric potential energy (UE) – energy
contained in a configuration of charges
 Increases when configuration becomes less
stable
 Decreases when configuration becomes
more stable
 Unit: Joule
Electric Potential Energy

Work must be done on the charge to increase
electric potential energy
For a positive test
charge to be moved
upward a distance d,
the electric force
does negative work
 The electric potential
energy has increased
and ΔU is positive

Work and Energy
If a negative charge
is moved upward a
distance d, the
electric force does
positive work.
 The change in the
electric potential
energy (ΔU) is
negative

Electric POTENTIAL

Electric potential (commonly called
VOLTAGE) is related to both electric
potential energy, and the electric field
 Units are the Volt, where 1V = 1 J/C

Change in potential energy is directly
related to change in voltage:
 ΔU = qΔV
○ Δ U is the change in electrical PE (unit: J)
○ q is the charged moved (unit: C)
○ Δ V is the potential difference (V)
Electric Potential & Potential
Energy

All charges will spontaneously go to
lower potential energies if allowed to
move – they try to decrease UE
Positive charges like to DECREASE
their potential (Δ V < 0)
 Negative charges like to INCREASE
their potential (Δ V > 0)

Practice #1

A 3.0 C charge is moved through a
potential difference of 640 V. What
is its change in potential energy?
Sample Problem
A 3.0 μC charge is moved through a potential difference of
640 V. What is its potential energy change?
Electric Potential in Uniform
Fields


The electric potential is related to a uniform
electric field:
Δ V = -Ed
 Δ V is the change in electric potential (V)
 E is a constant electric field strength
 d is the distance moved (m)
Practice Problem #2

An electric field is
parallel to the xaxis. What is the
magnitude and
direction of the
electric field if the
potential
difference
between x = 1.0m
and x = 2.5m is
found to be
+900V?
Sample Problem
An electric field is parallel to the x-axis. What is its
magnitude and direction if the potential difference
between x =1.0 m and x = 2.5 m is found to be +900 V?
Charges on Conductors

Excess charges
reside on the
surface of a
charged
conductor

If excess charges
were found inside
a conductor, they
would repel one
another until the
charges were as
far from each
other as possible –
on the surface
Electric Fields & Conductors

Electric field lines
are more dense
near a sharp
point – this
means the field
is more intense in
these regions


Lightning rods have a
sharply pointed tip
During an electrical
storm, the electric field
at the tip becomes so
intense that charge is
given off into the
atmosphere, discharging
the area near a building
at a steady rate and
preventing sudden blasts
of lightning
Electric Fields and
Conductors


The electric field inside a
conductor MUST be zero
If a conductor is placed in
an electric field, the
charges polarize to nullify
the external field
Conservation of Energy

Conservative
forces conserve
energy –
mechanical
energy changes
from one form to
another

When only the
conservative
electrostatic force
is involved, a
charged particle
released from rest
in an electric field
will transform
potential energy
into kinetic energy
Practice #5

A proton is accelerated through a potential
difference of -2,000 V. What is its change in
potential energy?

How fast will it be moving if it started at rest?
Sample Problem
If a proton is accelerated through a potential difference of
2,000 V, what is its change in potential energy?
How fast will this proton be moving if it started at rest?
#6

A proton at rest is released in a uniform electric
field. How fast is it moving after it travels
through a potential difference of -1200 V?
Sample Problem
A proton at rest is released in a uniform electric field. How
fast is it moving after it travels through a potential
difference of -1200 V? How far has it moved?
Electric Potential Energy

For spherical/point charges:
U
= kq1q2/r
 U is electrical PE (J)
 K is 9 x 109 Nm2/C2
 q1 and q2 are charges (C)
 r is the distance between centers (m)
#7

How far must the point
charges q1 = +7.22 C and
q2 = -26.1 C be separated
for the electric potential
energy of the system to be
-126 J?
Absolute Electric Potential
 For
a spherical/point charge, the
electric potential can be calculated
by:
 V = kq/r
 V is potential (V)
 k = 9 x 10^9
 q is charge (C)
 r is distance from the charge (m)
#8

The electric
potential 1.5 m from
a point charge q is
+2.8 x 104 V. What is
the value of q?
More about Electric Fields &
Electric Potential
E

= -ΔV/d
The electric field points
in the direction of
decreasing electric
potential

The electric
field is always
perpendicular
to the
equipotential
surface
E and Equipotential are
Perpendicular!

No work is done when a
charge is moved
perpendicular to an
electric field


If no work is
done, there is
no change in
potential
Potential is
constant in a
direction
perpendicular
to the electric
field
Equipotential Surfaces
No. NINE

Draw field lines for the charge configuration below.
The field is 600 V/m, and the plates are 2m apart.
Label each plate with its proper potential, and draw
and label 3 equipotential surfaces between the
plates. (Ignore edge effects)
Sample Problem
Draw field lines for the charge configuration below. The field is 600
V/m, and the plates are 2 m apart. Label each plate with its proper
potential, and draw and label 3 equipotential surfaces between the
plates. You may ignore edge effects.
- - - - - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -
++++++++++++++++++++++++++++++++
Ten

Draw a negative point charge of –Q
and its associated electric field.
Draw 4 equipotential surfaces such
that ΔV is the same between the
surfaces, and draw them at the
correct relative locations. What do
you observe about the spacing
between the surfaces?
Sample Problem
Draw a negative point charge of -Q and its associated electric field.
Draw 4 equipotential surfaces such that DV is the same between
the surfaces, and draw them at the correct relative locations. What
do you observe about the spacing between the equipotential
surfaces?