Physics 121: Electricity

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Physics 121 Electricity Magnetism Lecture
2Electric Charge

• Dale E. Gary
• Wenda Cao
• NJIT Physics Department

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Electricity in Nature

• Most dramatic natural electrical phenomenon is
  lightning.
• Static electricity (balloons, comb paper, shock
  from a door knob)
• Usesphotocopying, ink-jet printing

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Static Charge

• 1. How can I demonstrate static charge using an
  inflated balloon?
• Pop it. The sound it makes is due to static
  charge.
• Rub it on cloth, rug, or hair, then it will stick
  to a wall.
• Rub it on a metal surface, then use it to pick up
  bits of paper.
• Drop it and time its fall. If it falls slower
  than a rock, it is affected by static charge.
• Let the air out slowly. It will be larger than
  its original size due to static charge.

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Demonstrations of Electrostatics

• Balloon
• Glass rod/silk
• Plastic rod/fur
• Electroscope
• Van de Graaf Generator

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Glass Rod/Plastic Rod

• A glass rod rubbed with silk gets a positive
  charge.
• A plastic rod rubbed with fur gets a negative
  charge.
• Suspend a charged glass rod from a thread, and
  another charged glass rod repels it.
• A charged plastic rod, however, attracts it.
• This mysterious force is called the electric
  force.
• Many similar experiments of all kinds led
  Benjamin Franklin (around 1750) to the conclusion
  that there are two types of charge, which he
  called positive and negative.
• He also discovered that charge was not created by
  rubbing, but rather the charge is transferred
  from the rubbing material to the rubbed object,
  or vice versa.

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Forces Between Charges

• We observe that

Like charges repel each other
Opposite charges attract each other
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Electroscope

• This is a device that can visually show whether
  it is charged with static electricity.
• Here is an example charged positive.
• Notice that the charges collect near the ends,
  and since like charges repel, they exert a force
  sideways.

- - - - - -

• You can make the deflection arm move by adding
  either positive or negative charge.
• BUT, we seem to be able to make it move without
  touching it.
• What is happening?

Electrostatic Induction
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The Atom

• We now know that all atoms are made of positive
  charges in the nucleus, surrounded by a cloud of
  tiny electrons.

Proton charge e, electron charge -e where e
1.602?10-19 C
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The Atom

• We now know that all atoms are made of positive
  charges in the nucleus, surrounded by a cloud of
  tiny electrons.

• Atoms are normally neutral, meaning that they
  have exactly the same number of protons as they
  do electrons.
• The charges balance, and the atom has no net
  charge.

Electron
Proton

• 2. Which type of charge is easiest to remove
  from an atom?
• Proton
• Electron

Proton charge e, electron charge -e where e
1.602?10-19 C
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The Atom

• In fact, protons are VASTLY more difficult to
  remove, and for all practical purposes it NEVER
  happens except in radioactive materials. In this
  course, we will ignore this case. Only electrons
  can be removed.

• 3. If we remove an electron, what is the net
  charge on the atom?
• Positive
• Negative

If we cannot remove a proton, how do we ever make
something charged negatively? By adding an
extra electron.
Proton charge e, electron charge -e where e
1.602?10-19 C
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Glass Rod/Plastic Rod Again

• We can now interpret what is happening with the
  glass/plastic rod experiments.
• Glass happens to lose electrons easily, and silk
  grabs them away from the glass atoms, so after
  rubbing the glass becomes positively charged and
  the silk becomes negatively charged.
• Plastic has the opposite tendency. It easily
  grabs electrons from the fur, so that it becomes
  positively charged while the fur becomes
  negatively charged.

The ability to gain or lose electrons through
rubbing is called Triboelectricity.
Tribo means rubbing
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Triboelectric Series
asbestos rabbit fur glass hair nylon wool
silk paper cotton hard rubber synthetic
rubber polyester styrofoam orlon saran
polyurethane polyethylene polypropylene
polyvinyl chloride (PVC pipe) teflon silicone
rubber
Most Positive (items on this end lose electrons)
Most Negative (items on this end steal electrons)
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Insulators and Conductors

• Both insulators and conductors can be charged.
• The difference is that
• On an insulator charges are not able to move from
  place to place. If you charge an insulator, you
  are typically depositing (or removing) charges
  only from the surface, and they will stay where
  you put them.
• On a conductor, charges can freely move. If you
  try to place charge on a conductor, it will
  quickly spread over the entire conductor.

Insulator
Conductor
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Insulators and Conductors

• 4. Which of the following is a good conductor of
  electricity?
• A plastic rod.
• A glass rod.
• A rock.
• A wooden stick.
• A metal rod.

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Metals and Conduction

• Notice that metals are not only good electrical
  conductors, but they are also good heat
  conductors, tend to be shiny (if polished), and
  are maleable (can be bent or shaped).
• These are all properties that come from the
  ability of electrons to move easily.

This iron atom (26 protons, 26 electrons) has two
electrons in its outer shell, which can move from
one iron atom to the next in a metal.
Path of electron in a metal
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Van de Graaf Generator

• Rubber band steals electrons from glass

• Glass becomes positively charged

• Rubber band carries electrons downward

• Positively charged glass continues to rotate

• Wire brush steals electrons from rubber band

• Positively charged glass steals electrons from
  upper brush

• Sphere (or soda can) becomes positively
  chargedto 20,000 volts!

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Electric Force and Coulombs Law

• We can measure the force of attraction or
  repulsion between charges, call them q1 and q2
  (we will use the symbol q or Q for charge).
• When we do that, we find that the force is
  proportional to the each of the charges, is
  inversely proportional to the distance between
  them, and is directed along the line between them
  (along r).
• In symbols, the magnitude of the force is
  where k is some constant of
  proportionality.
• This force law was first studied by Coulomb in
  1785, and is called Coulombs Law. The constant
  k 8.98755?109 N m2/C2 is the Coulomb constant.

q1
q2
r
q1
q2
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Electric Force and Coulombs Law

• Although we can write down a vector form for the
  force, it is easier to simply use the equation
  for the magnitude, and just use the like charges
  repel, opposites attract rule to figure out the
  direction of the force.
• Note that the form for Coulombs Law is exactly
  the same as for gravitational force between two
  masses
• Note also that the mass is an intrinsic property
  of matter. Likewise, charge is also an intrinsic
  property. We only know it exists, and can learn
  its properties, because of the force it exerts.
• Because it makes other equations easier to write,
  Coulombs constant is actually written
  
• where e0 8.85?10-12 C2/N-m2 is called the
  permittivity constant.

Note BIG difference, There is only one sign of
mass, only attraction.
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Spherical Conductors

• Because it is conducting, charge on a metal
  sphere will go everywhere over the surface.
• You can easily see why, because each of the
  charges pushes on the others so that they all
  move apart as far as they can go. Because of the
  symmetry of the situation, they spread themselves
  out uniformly.
• There is a theorem that applies to this case,
  called the shell theorem, that states that the
  sphere will act as if all of the charge were
  concentrated at the center.

Note, forces are equal and opposite
These two situations are the same
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Insulators and Conductors

• 5. Two small spheres are charged with equal and
  opposite charges, and are placed 30 cm apart.
  Then the charge on sphere 1 is doubled. Which
  diagram could be considered to show the correct
  forces?

-q
2q
A. B. C. D. E.
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Case of Multiple Charges

• You can determine the force on a particular
  charge by adding up all of the forces from each
  charge.

Forces on one charge due to a number of other
charges
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Charges in a Line

• 6. Where do I have to place the charge in order
  for the force to balance, in the figure at right?
• Cannot tell, because charge value is not given.
• Exactly in the middle between the two negative
  charges.
• On the line between the two negative charges, but
  closer to the -2q charge.
• On the line between the two negative charges, but
  closer to the -q charge.
• There is no location that will give force
  balance.

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Lets Calculate the Exact Location

• Force is attractive toward both negative charges,
  hence could balance.
• Need a coordinate system, so choose total
  distance as L, and position of charge from -q
  charge as x.
• Force is sum of the two force vectors, and has to
  be zero, so
• A lot of things cancel, including Q, so our
  answer does not depend on knowing the charge
  value. We end up with
• Solving for x, , so
  slightly less than half-way between.

L
x
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Summary

• Charge is an intrinsic property of matter.
• Charge comes in two opposite senses, positive and
  negative.
• Mobil charges we will usually deal with are
  electrons, which can be removed from an atom to
  make positive charge, or added to an atom to make
  negative charge. A positively charged atom or
  molecule can also be mobil.
• There is a smallest unit of charge, e, which is e
  1.602?10-19 C. Charge can only come in units
  of e, so charge is quantized. The unit of charge
  is the Coulomb.
• Charge is conserved. Charge can be destroyed
  only in pairs (e and e can annihilate each
  other). Otherwise, it can only be moved from
  place to place.
• Like charges repel, opposite charges attract.
• The electric force is give by Coulombs Law
• Materials can be either conductors or insulators.
• Conductors and insulators can both be charged by
  adding charge, but charge can also be induced.
• Spherical conductors act as if all of the charge
  on their surface were concentrated at their
  centers.