Electric Forces and Fields
Electric Charge
• Let’s review…
• Atoms consist of:
– Protons, neutrons,
electrons
• Protons have a charge
of:
– +e
What is e?
e=1.6 x 10-19C
Unit is the coulomb (C)
This is the smallest charge
yet discovered.
• Electrons have a charge
of
– -e
• Neutrons have a charge
of 0
Electric
Charge
• Intrinsic property of
electrons and protons
• Most objects have
balanced charges- in
order to carry a charge,
there must be an
imbalance btwn p+ and
e- (ionization)
• Can be positive or
negative
• Likes repel
• Opposites attract
Electric Charge is…
• Charge is
conserved- net
charge cannot be
created or destroyed
• Charge is
quantized- must be
an integer multiple
of e
• q= the charge of an
object (unit is C)
Creating Electric Charge
• Usually charge is created
through transfer of
electrons
• Gain electrons = gain
negative charge
• Lose electrons= gain
positive charge
• You can do this in 3
ways:
– Friction
– Conduction
– Induction
Charging by
friction
• Different objects have
different propensities for
gaining or losing
electrons
• Triboelectric sequence
ranks objects-if you rub
any 2 objects together,
the one on top will lose
elecrons and the one on
the bottom will gain
• The farther they are
apart, the more they will
charge
Asbestos
Fur (rabbit)
Glass
Mica
Wool
Quartz
Fur (cat)
Lead
Silk
Human skin, Aluminum
Cotton
Wood
Amber
Copper, Brass
Rubber
Sulfur
Celluloid
India rubber
Charging by friction
• Using the triboelectric sequence, predict what will
happen when a glass rod is rubbed on a piece of silk
• Will a charge develop?
• How big will it be?
• Which object will be negative?
Charging by Conduction
• Conduction=
TOUCHING
• If you touch a
charged object to
another object,
electrons can
actually flow from
one to the other
Showing Conduction
• We can use an electroscope to show charging by
conduction
• Take a positively charged rod and touch it to the ball
on the top of the electroscope
Electroscope
• Which way would electrons flow?
• What would be the residual charge on the shows SAME
charge after
electroscope?
conduction
Charging by Induction
• Charged object is
brought near but never
touches another object
• Because electric charge
does not require contact
(electric field), you can
induce a charge just by
proximity with a
charged object
Showing Induction
• If you bring your + rod near the electroscope,
electrons will be attracted to it and will gather at the
ball- this is temporary- once you move it away, the
charge is gone
• However, if the electroscope is grounded (attached
to the earth which is a pretty good conductor) you
could get electrons flowing from the earth and keep a
net charge- opposite to charging rod!
Induction in insulators
• In an insulator, electrons can’t move freely
• You can still induce a charge by polarizing
the molecules close to the charged object
In this insulator the top
surface becomes - and the
bottom surface becomes +
Induction in insulators
• Try this with a charged rod and tiny
scraps of paper (an insulator)
• What happens to the paper? Why?
• What processes are happening?
Coulomb’s Law
• Electrostatic force,
Fe depends on
• The charge on the
objects: q1 and q2
• The distance
between them, r
Coulomb’s Law
• For point charges
• F=k q1q2
r2
• On your green sheet, k is written as:
• k= 1/40 but in the section on constants, you
can find k- look it up now
• Easiest to deal with magnitudes of q and then
note that likes repel, opposites attract
Coulomb’s Law, visually
Example: Coulomb’s Law
• Consider 2 small spheres, one carrying
a charge of +1.5nC and the other a
charge of -2.0nC, separated by a
distance of 1.5cm. Find the electric
force between them.
• (reminder: nano=10-9)
Solution: Coulomb’s Law
• FE=kq1q2/r2
• =(9x109Nm2/C2) (1.5x10-9C)(-2.0x10-9C)
(0.015m)2
• =-1.2x10-4N
• When F is -, it means attraction…but
you knew that already by the opposite
charges
• Worksheet: Coulomb’s Law
Superposition and Coulomb
• If there are more
than 2 point
charges, the FE is
the sum of all FE
acting on a point
Worksheet: Coulomb Beyond
the Fundamentals
and Suspended spheres
The Electric Field
Electric Field
E=Fon q/q
The Electric field equals the
electric force on a small test
charge, q, divided by that
small test charge.
Unit: N/C
Direction: same as force
• The presence of a
charge created an
electric field in the
space that surrounds it
• Other charges will be
affected by this field
• Directional so it is a
vector and can be
added/subtracted as a
vector
The electric field leads to the F
Putting it together: FE and E
• FE=kq1q2/r2
• E=Fon q/q
E=Fon q/q
E=kqQ
r 2q
E=kQ/r2
Note- not on green sheet.
You will need to be able to
derive this if you need it!
Electric Field Lines
Begin at +, end at -, do not start or stop in midspace, number of
lines is proportional to the charge.
• Point in for -source
• Point out for
+source
• Density of lines
shows strength of
field
Distance and Strength of E
Vector Nature of E
At any point, you can add the EB+EA
Vector Addition of E
Common E interactions
• Note direction of arrows
• 2 equal but opposite charges (above right)
are called an electric dipole
• NOTICE- fields lines NEVER CROSS
Electric Field Example
• A charge of q=+3.0nC is placed at a
location at which the electric field has a
strength of 400N/C. Find the force felt
by the charge q.
Electric Field Solution
• Fon q=qE
• F=(3x10-9C)(400N/C)=1.2x10-6N
• Worksheet: Electrostatic Forces and
Fields: Point Charges
Conductors and Insulators
•
•
•
•
Conductors permit the flow of excess charge
Insulators don’t let electrons flow
Semiconductors- kind of in between
Superconductors- no resistance to flow of
electrons (many metals act this way at low T)
Conductors- a closer look
• Any excess charge resides solely on the outer
surface of a conductor
• The charge inside is zero!
• Any LOST fans? Michael Faraday built a “room
within a room” to demonstrate this- the man in the
picture is safe- no charge inside his cage
• We use this to “shield” our sensitive electronics by
enclosing in a metal box
Faraday Cage
Conductors- a closer look
• For points outside the
conductor, the electric
field acts as if it is
concentrated at the
center of the conductor
• Electric field is always
perpendicular to the
surface
– No matter what the
shape
Special Situations: Parallel Plates
• Above you see 2 parallel plates attached
to a battery
• The symbol on the left is the battery- the
longer line is the + terminal and the
shorter line is the –
• Thus the top plate is + and bottom is –
• The electric field then is the the direction
a + charge would move- thus the arrows
Special Situations: Parallel Plates
• This type of field is
uniform
• In parallel plates,
E=V/d where V is
voltage supplied by
battery and d is
distance between
plates
• (units of V/m= N/C)
for E
• Thus a test
charge would
experience the
same force
regardless of
where it is located
in the field
• F=qE
ANYWHERE
between plates
Example: Parallel Plates
• V=28V and d=0.14 m
• Find the F on a 2nCcharge inserted
anywhere between the plates
Plates problem solution
•
•
•
•
1st find E:
E=28V/0.14m
E=200V/m
Or 200 N/C
•
•
•
•
•
2nd find F
F=qE
F=(2x10-9C)(200N/C)
F=4 x 10-7N
TOWARD which
plate?