Static Electricity,
Electric Forces,
Electric Fields,
Electric Potential Energy,
Electric Potential,
Capacitors
Electric Charges
•
•
•
•
Electrons have a negative charge
Protons have a positive charge
Charge is measured in “coulombs”
“q” or “Q” in an equation is used for
charge
• 1 electron has 1.6 x 10-19 C of charge
Static Electricity
• Static Electricity is the study of
“charges at rest”.
• Fundamental Rule of Charge
– Opposite charges attract,
– Like charges repel
• 3 methods of charging :
friction, conduction, & induction
• Conductors allow electrons to move
freely, Insulators do not!
Methods of Charging
• Charging by friction scrapes electrons off one object and
places them on the other (the two objects will have equal
and opposite charges)
• Charging by induction requires no contact. A charged
object is brought near a neutral object and the charges in
the neutral object become polarized (opposites attract and
likes repel) so that neutral object behaves as if it is charged
(but really it still has same # of + & - charges, so still
neutral)
• Charging by conduction requires contact. A charged
object comes in contact with a neutral object and charges
are transferred between objects until they both have equal
charge (charge equilibrium)
Electrostatic Forces (F)
(measured in Newtons)
Given 2 charges of magnitude q1 & q2 separated by a distance d, the
magnitude of the force that each of the charges exerts on the other is
calculated by the relationship given by Coulomb’s Law. The
direction of the force is determined by the fundamental law of
charges (i.e. attraction or repulsion). The forces must be equal and
opposite … Newton’s 3rd Law!
q1
F
F
+
Coulomb’s Law:
q2
-
d
F
F
+
+
q1
q2
k = 9 x 109 N*m2/C2
kq1q2
F
2
d
This is known as “Coulomb’s constant”
Electric Fields (E)
measured in Newtons per Coulomb
• Electric fields are the “energy field” that surrounds any
charged particle”
• Any other charge in this field will experience a force.
• Electric fields are vectors (mag. & dir.)
• The direction of an Electric field is defined by the
direction of the force on a “+” test charge placed in
that field, thus Electric fields are always in a direction
that is away from “+” and toward “-”.
• Electric Field strength is measured in units of N/C
(newtons per coulomb)
Electric Field due to a Point Charge
To calculate the Electric Field strength,
E, at a point “x” a distance, d, from the
charge, q, creating the electric field, use
the following formula...
kq
E 2
d
x
d
q
-
Field around a
Negative charge
q
+
Field around a
Positive charge
Force on a charge due
to an Electric Field
If a charge, q, is placed at point “x” in the field
where the Electric Field strength is E, it will
experience a force F.
F  qE
F
E
q
F
E
+
q
d
Q
+
Electric Potential Energy (Uelec)
measured in Joules
When two charges are placed near each other, they have the
potential to start moving under the influence of the force
between them. If they have the “potential” to have “kinetic
energy” then according to the Law of Conservation of
Energy, they must have Potential Energy when they are in
that arrangement. To calculate the potential energy of this
arrangement of charges…
q1
+
q2
d
U elec
kq1q2

d
Remember: energy of any kind is always a scalar quantity…magnitude only!
Electric Potential (V)
measured in Volts
• Electric Potential (V) is defined as the Electric Potential Energy
(Uelec) per unit of charge (q) at a given point in an Electric Field.
• Electric Potential (V) is a scalar quantity, so…magnitude only
but may be positive or negative based on the sign of the charge
creating the field.
• 1 volt = 1 joule per coulomb (1 V=1 J/C)
To calculate the electric potential at a
point in space due to a single point
charge, use…
U elec kQ
V


…where Q is the charge creating the
q
d
field and q is any charge that might be
at the point in space of interest.
Equipotential Lines
• Equipotential lines are “lines of equal energy”
• All points on each line have the same electric
potential (V)
• Equipotential lines are usually parallel to the
surface of the charge
• They do not depend on the sign of the charge
For a point charge,
they are concentric
circles.
q
Equipotential lines,
each line has a
different potential (V)
Uniform Electric Fields
+Q
+
E
-Q
-
+
-
+
-
+
-
+
-
d
V1
V2
ΔV = V1-V2
Uniform Electric fields exist when there are equal
and oppositely charged plates separated by a
distance, d. Each charged plate has a different
value of electric potential (V1 and V2), often
determined by connecting the plates to the
terminals of a battery. The individual values of
electric potential (V) are not important but the
potential difference between the plates (ΔV) is
very important. The electric fields created by
each charged plate combine such that total electric
field that has a constant value (E) at all regions
between them. The relationship between the
potential difference, V, electric field, E, and
distance, d is…
V  Ed
Note: This formula is ONLY
valid for uniform fields!
Work done moving a charge through
an Electric Field (W) - measured in Joules
V2
q
V1
+
-
+
-
+
-
V1
V2
+
-
+
-
If a charge is moving through an electric field,
it experiences a force in the direction of the
field that pushes it across equipotential lines.
The charge moves through a distance, d,
between its starting and final points and has a
different potential (V) at the beginning and end,
thus ΔV. Since there is a force moving an
object through a distance, work is done on the
charge. The following relationships apply.
W  Fd , and F  qE
so... W  qEd, also
V  Ed, so...
W  qV
Capacitors
• A device used to store charge (energy)
• Made of 2 conductors separated by an
insulator
• Each conductor carries an equal but
opposite charge, q
• Releases all charge (stored energy) in one
big burst…think camera flash!
Capacitance (C)
measured in farads
• Capacitance is the quantity that describes the
ability of a capacitor to store energy in the
form of electric charge.
• Or…The capacitance is the capacity of the
capacitor
• Capacitance depends on the amount of charge
stored on each plate and the potential
difference between the plates.
• It is measured in units of Farads (F), named for
Michael Faraday (a famous Physicist).
To calculate the capacitance,
C, simply find the ratio of
the charge stored on a single
plate, Q, and the potential
difference between the
plates, ΔV.
Note: 1 Farad = 1 Coulomb / Volt
Also, a Farad is a very large unit so usually
use μF (10-6), nF (10-9), or pF (10-12).
Q
C=
V
An example of a simple capacitor:
(parallel-plate capacitor)
2 oppositely charged plates
+
E
-
To get more stored charge:
+
-
• increase the size of the plates
+
-
• decrease the plate separation
+
-
• increase the voltage of the battery
+
-
battery
+
-
Insulator such as air,
paper, plastic, or mylar