Static Electricity,
Electric Forces,
Electric Fields
Static Electricity
• Static Electricity involves 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 – two neutral objects are rubbed
together and become oppositely charged ( the object that
gains electrons becomes negatively charged and the one
that loses electrons becomes positively charged)
• Charging by induction – a charged object is brought near
but not touching a neutral object ( the neutral object gets a
temporary charge separation – gets opposite charge near
the charged object)
• Charging by conduction – a charged object touches a
neutral object so charges are transferred between objects
until they reach charge equilibrium, ie. have equal charge
(the neutral object gets the same charge)
Electric Forces
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 using Coulomb’s Law. The forces can be attractive or
repulsive and must be equal and opposite … Newton’s 3rd Law!
Coulomb’s Law:
kq1q2
FE 
2
d
q1
q2
+ F
F
d
F
F
+
+
q1
q2
FE = electrostatic force, Newtons (N)
k = electric or Coulomb’s constant = 9 x 109 Nm2/C2
q1
= charge of the first object, C q2 = charge of the second object, C d
= distance between the two charges (center to center), m
Electric Charges
• Electrons have a negative charge
• Protons have a positive charge
• Charge is measured in “coulombs”
• “qo” or “Q” in an equation is used
for charge
• 1 electron has -1.6 x 10-19 C of
charge
Electric Fields
• Electric fields are the “energy fields” that surrounds any charged
particle”
• Any charge placed in this field will experience a force.
• Electric fields are vectors (magnitude & direction).
• The direction of an electric field is defined by the direction of
the force on a tiny “+” test charge placed in that field. Thus
electric fields are always in a direction that is away from “+”
and toward “-”.
• Electric Field strength is the force per unit charge and is
measured in units of N/C (Newtons per Coulomb)
F
E
qo
E = Electric Field Strength, N/C
F = Electrostatic Force, N
qo = Charge placed in the electric field, C
Electric Field around a Charge
Field around a
Negative charge
Field around a
Positive charge
-
+
Note - In the formulas on the previous
slide and on the following slides q0 and Q
are described as follows:
Q = charge of the object causing
the electric field, C
qo = test charge or the charge of
the object placed in the field, C
Electric Field Strength
at a point near a charge
kqoQ
2
F
kQ
d
E

 2
qo
qo
d
Q
+
.
E
d
E= electric field strength, N/C
k = electric or Coulomb’s constant (9 x 109)
Q = charge causing the field, C
d = distance from the charge to where the field
strength is being measured, m
Electric Potential Difference
• Electric Potential Difference is the potential energy per
unit charge at a given point due to an electric field.
• Units: Volts (1 volt = 1 Joule per Coulomb)
• Potential Difference is required to make current flow.
PE
V 
qo
ΔV = Electric Potential Difference, Volts
ΔPE =change in electric potential energy, J
qo= charge placed in an electric field, C
Note: 1 Volt = 1 Joule / Coulomb
Potential Difference at a Point
kqoQ
d
2
PE Fd
kQ
d
V 



qo
qo
qo
d
kQ
VP 
d
Q
d
.
ΔVP = Potential Difference at a point, V
k = Coulomb’s constant = 9 x 109 Nm2/C2
Q = Charge causing the electric field, C
VP
d = distance between Q and where VP is
being measured, m
Electric Potential Energy
between 2 charges
kq1q2
PE  W  Fd  2  d 
d
kq1q2
PE 
d
q1
d
q2
Work done on a charge
PE W
V=

qo
qo
So:
W=qo ΔV
• W- the work required to move a charge
through a potential difference, Joules (J)
• qo - magnitude of the charge placed in the
field, Coulombs (C)
•  V - potential difference, Volts (V)
Electric Potential of a charge moving
in a uniform electric field
ΔV=Ed
∆V = electric potential difference, V
E = electric field strength, V/m or N/C
d = displacement moved along the field lines, m
Note: It must be a uniform electric field! Also there is no ∆PE and
thus no ∆V if displacement is perpendicular to the electric field.
Capacitor – a device used to
store charge. Example of a
common simple 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
+
-
Note: This is an example of a
uniform electric field.
Insulator such as air
Capacitance – the ability of a
conductor to store energy in the form
of electrically separated charges
Q
C=
V
C = Capacitance, Farads (F)
Q = charge on one plate, C
∆V = Potential difference, V
Note: 1 Farad = 1 Coulomb / Volt
Also, a Farad is a very large unit so usually use μF or pF.
(micro = μ = 10-6, nano = n = 10-9, pico = p = 10-12)
Electrostatics Formulas
kq1q2
PE 
d
kQ
VP 
d
kq1q2
FE 
d2
kQ
E 2
d
F
E
qo
V 
ΔV=Ed
C=
PE
qo
Q
V
W  qo V
PEC  1
2
 C  V 
2
Note: The top two and next two equations look alike except for
d2 vs d. The ones on the left are vector quantities and have d2
while the ones on the right have d and are not vectors.