Electrostatics

1
Electrostatics

• NCSSM - PH. 354
• March, 2006
• Gabriela Stefan

2
Objectives

• After studying this chapter, you should
• know the different types of electric charge and
  the magnitude of the smallest available charge.
• know the difference between insulators and
  conductors.
• be able to use Coulomb's law and apply it to
  situations involving many charges.

3
Charge

• http//www.dl.ket.org/physics/companion/ThePC/comp
  an/estat/pos2pith.htm
• there are two kinds of charge, positive and
  negative
• like charges repel, unlike charges attract
• positive charge comes from losing electrons
  negative charge comes from gaining electrons
• charge is quantized, meaning that charge comes in
  integer multiples of the elementary charge e
• q n e
• q is the symbol used to represent charge, while n
  is a positive or negative integer, and e is the
  electronic charge, 1.60 x 10-19 Coulombs.
• charge is conserved in isolated systems

4
Friction

• Charging two different materials using a wool
  cloth
• http//www.regentsprep.org/Regents/physics/phys03/
  aeleclab/chargstp.htm

5
Conduction

• An electroscope is a device used to detect the
  presence of charge and it's relative amount.  One
  method of charging the electroscope is by
  conduction or contact.  This means that a charged
  object must actually touch the electroscope and
  transfer charge too.  If the electroscope returns
  to normal after being touched by the charged
  object then it is quite possible that the charged
  object is so weakly charged that it is not
  willing to share its excess charge with the
  electroscope.
• When charging something by contact it is
  important to note the following properties
• The objects must actually touch and transfer some
  electrons.
• The objects become charged alike.
• The original charged object becomes less charged
  because it actually lost some charge.  Therefore,
  there is a limit to how many times it could be
  used to charge something without being recharged.

6
Inducing a Positive Charge on a Sphere

• The induction process is characterized by the
  following general features
• A charged object is needed to charge an object by
  induction. Yet there is never any contact made
  between the charged object and the object being
  charged.
• Only conductors can be charged by the induction
  process. The process relies on the fact that a
  charged object can force or induce the movement
  of electrons about the material being charged.
• The object being charged ends up with a charge
  which is the opposite of the object being used to
  charge it.
• A ground must be used to create the charge on the
  object. The ground allows for electron movement
  into or out of the object being charged.

7
Charging a Two Sphere System by Induction

• http//www.physicsclassroom.com/mmedia/estatics/it
  sn.html

The induction process is characterized by the
following general features A charged object is
needed to charge an object by induction. Yet
there is never any contact made between the
charged object and the object being charged.
Only conductors can be charged by the induction
process. The process relies on the fact that a
charged object can force or induce the movement
of electrons about the material being charged.
The object being charged ends up with a charge
which is the opposite of the object being used to
charge it. A ground must be used to create the
charge on the object. The ground allows for
electron movement into or out of the object being
charged.
8
Electroscope

• When the positively-charged electroscope is
  touched, its charge becomes grounded (or
  neutralized). This is depicted in the animation
  to the right. The grounding process involves a
  transfer of electrons between the charged
  electroscope and the conducting object to which
  it is touched. When a positively-charged
  electroscope is touched, electrons enter the
  electroscope from the ground. Being positively
  charged, the electroscope attracts some electrons
  from the conducting material (in this case, a
  person). The negatively-charged electrons enter
  the electroscope and neutralize the positive
  charge. As the electroscope loses its charge, the
  needle relaxes back to its naturally upright
  position.

http//www3.ltu.edu/s_schneider/physlets/main/ele
ctroscope.shtml 1. Grounding a Positively
charged Electroscope
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2. Grounding a Negatively Charged Electroscope

• When the negatively-charged electroscope is
  touched, its charge becomes grounded (or
  neutralized). This is depicted in the animation
  to the right. The grounding process involves a
  transfer of electrons between the charged
  electroscope and the conducting object to which
  it is touched. When a negatively-charged
  electroscope is touched, electrons leave the
  electroscope to the ground. Since electrons repel
  other electrons, their tendency is to spread out
  as far as possible through any conductor. To
  excess electrons, the farther away that they can
  be from one another, the better. When touched by
  a larger conducting material (in this case, a
  person), the electrons have an opportunity to
  spread out even further by using the vast space
  of the ground. The excess electrons leave the
  electroscope, thus neutralizing its overall
  charge. As the electroscope loses its charge, the
  needle relaxes back to its naturally upright
  position.

10
Electrophorus

• Johannes Wilcke invented and then Alessandro
  Volta perfected the electrophorus over two
  hundred years ago. This device was quickly
  adopted by scientists throughout the world
  because it filled the need for a reliable and
  easy-to-use source of charge and voltage for
  experimental researches in electrostatics. A
  hand-held electrophorus can produce significant
  amounts of charge conveniently and repeatedly. It
  is operated by first frictionally charging a flat
  insulating plate called a "cake". In Volta's day,
  the cake was made of shellac/resin mixtures or a
  carnauba wax film deposited on glass. Nowadays,
  excellent substitutes are available. TeflonTM,
  though a bit expensive, is a good choice because
  it is an excellent insulator, charges readily,
  and is easy to clean and maintain. The
  electrophorus is ideal for generating energetic
  capacitive sparks.
• The electrophorus consists of a conductive
  (metal) electrode with an insulating handle and
  an insulating plate. Provision for grounding the
  electrode must be provided. First, the insulating
  plate is triboelectrically charged by rubbing it
  with a dry cloth. The resulting surface charge,
  while itself immobile, makes it possible to
  charge the electrode by induction.
  http//www.ece.rochester.edu8080/jones/jethberel
  /elphorus/electrophorus_iexplorer.htm

11
Coulombs Law

• The Parallel between Gravity and
  Electrostatics
• http//physics.bu.edu/duffy/semester2/c02_gravi
  ty.html
• Java Applets
• http//www.tamuk.edu/math/scott/physlets/Doc/Apple
  ts.htm
•   Third-law force pair between charges -
  Coulomb's Law   
• http//physics.bu.edu/duffy/semester2/c01_magnitu
  de.html
• Force vs Distance
• http//physics.bu.edu/duffy/semester2/c01_coul
  omb.html
• Coulombs Law with multiple discrete charges
• http//www3.ltu.edu/s_schneider/physlets/main
  /coulomb.shtml
• Dr. Hershfield University of Florida
• http//www.phys.ufl.edu/phy3054/elecstat/Welco
  me.html

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Inverse Square Laws

• Coulombs Law Newtons Law

SimilaritiesBoth the forces are directly
proportional to the product of the interacting
commodities (mass and charge) Both the forces
are inversely proportional to the square of the
distance of separation DifferencesThe
Coulombian force can be attractive or repulsive
while the gravitational force is attractive only
The magnitude of the Coulombian force depends
upon the medium separating the charges while the
gravitational force is independent of the medium
 
13
Principle of Superposition

• Electrical forces obey what is known as the
  principle of superposition.
• The electrical force acting on a test charge at
  position vector r is simply the vector sum of
  all of the Coulomb law forces from each of the N
  charges taken in isolation. In other words, the
  electrical force exerted by the j th charge
  (say) on the test charge is the same as if all
  the other charges were not there.
• Remember that force is a vector, so when more
  than one charge exerts a force on another charge,
  the net force on that charge is the vector sum of
  the individual forces.

14
Practice Problems

• 1. Suppose that two point charges, each with a
  charge of 1.00 Coulomb are separated by a
  distance of 1.00 meter. Determine the magnitude
  of the electrical force of repulsion between
  them. (Felect 9.0 x 109 N)
• 2. Two balloons are charged with an identical
  quantity and type of charge -6.25 nC. They are
  held apart at a separation distance of 61.7 cm.
  Determine magnitude of the electrical force of
  repulsion between them. (Felect 9.23 x 10-7 N)
• 3. Two balloons with charges of 3.37 µC and
  -8.21 µC attract each other with a force of
  0.0626 Newtons. Determine the separation distance
  between the two balloons. (d 1.99 m)

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Problems

• 4. The Q in Coulomb's law equation stands for
  the _____.
• a. mass of a charged object
• b. of excess electrons on the object
• c. the current of a charged object
• d. the distance between charged objects
• e. charge of a charged object
• 5. The symbol d in Coulomb's law equation
  represents the distance from ___.
• a. A to B b. A to D c. B to C d. B to D
  e. C to D f. A to G g. B to F h. C
  to E

16
Problems

• 6. Determine the electrical force of attraction
  between two balloons with separate charges of
  3.5 x 10-8 C and -2.9 x 10-8 C when separated a
  distance of 0.65 m.
•  
• 7. Determine the electrical force of attraction
  between two balloons with opposite charges but
  the same quantity of charge of 6.0 x 10-7 C when
  separated a distance of 0.50 m.
•  
•  
• 8. A balloon has been rubbed with wool to give
  it a charge of -1.0 x 10-6 C. A plastic rod with
  a charge of 4.0 x 10-6 C localized at a given
  position is held a distance of 50.0 cm above the
  balloon. Determine the electrical force of
  attraction between the rod and the balloon.
•  

17
Problems

• 9. A balloon with a charge of 4.0 µC is held a
  distance of 0.70 m from a second balloon having
  the same charge. Calculate the magnitude of the
  repulsive force.
•   
• 10. At what distance of separation must two
  1.00-microCoulomb charges be positioned in order
  for the repulsive force between them to be
  equivalent to the weight of a 1.00-kg mass?
• 11. A sphere with charge 6.0 µC is located near
  two other charged spheres. A 3.0 µC sphere is
  located 4.00 cm to the right and a 1.5 µC sphere
  is located 3.00 cm directly underneath. Determine
  the net force on the 6.00 µC sphere.

18
Problems

• 12. How many coulombs of charge are on the
  electrons in a nickel? Use the following method
  to find the answer.
• A. Find the number of atoms in a nickel. A nickel
  has a mass of about 5g. Each mole (6.02 x 10 23
  atoms) has a mass of about 58g.
• B. Find the number of electrons in the coin. A
  nickel is 75 Cu and 25 Ni, so each atom on
  average has 28.75 electrons.
• C. Find how many coulombs of charge are on the
  electrons.
• P3 page 478 Problems 30, 31, 32, 33, 34
• 13. A 0.90-gram balloon with a charge of -75 nC
  is located a distance of 12 cm above a plastic
  golf tube which has a charge of -83 nC. How could
  one apply Newton's laws to determine the
  acceleration of the balloon at this instant? (a
  5.5 m/s/s, down)

19
Problems

• 14. A positively-charged object with a charge of
  85 nC is being used to balance the downward
  force of gravity on a 1.8-gram balloon which has
  a charge of -63 nC. How high above the balloon
  must the object be held in order to balance the
  balloon? (NOTE 1 nC 1 x 10 -9 C) (r0.155
  meters )
• 15. Balloon A and Balloon B are charged in a like
  manner by rubbing with animal fur. Each acquires
  an excess of 25 trillion electrons. If the mass
  of the balloons is 1 gram, then how far below
  Balloon B must Balloon A be held in order to
  levitate Balloon B? Assume the balloons act as
  point charges. (r 3.83 meters )
• 16. Two 1.2-gram balloons are suspended from
  light strings attached to the ceiling at the same
  point. The net charge on the balloons is -540 nC.
  The balloons are distanced 68.2 cm apart when at
  equilibrium. Determine the length of the string.
  (r 78.8 cm )

20
Problems

• 17. ZINGER Three charges are placed along the
  X-axis. Charge A is a 18 nC charge placed at the
  origin. Charge B is a -27 nC charge placed at the
  60 cm location. Where along the axis (at what
  x-coordinate?) must positively-charged C be
  placed in order to be at equilibrium? (x -267
  cm)

• 18. Two 1.1-gram balloons are suspended from
  2.0-meter long strings and hung from the ceiling.
  They are then rubbed ten times with animal fur to
  impart an identical charge Q to each balloon. The
  balloons repel each other and each string is
  observed to make an angle of 15 degrees with the
  vertical. Determine the electric force of
  repulsion, the charge on each balloon (assumed to
  be identical), and the quantity of electrons
  transferred to each balloon as a result of 10
  rubs with animal fur.
• (Felect 0.00289 N) (Q 5.87 x 10-7 C
  (negative) ) ( excess electrons 3.67 x 1012
  electrons )

21
Problems

• 19. Four charges are arranged in a square with
  sides of length 2.5 cm. The two charges in the
  top right and bottom left corners are 3.0 x 10
  -6 C. The charges in the other two corners are
  -3.0 x 10-6 C. What is the net force exerted on
  the charge in the top right corner by the other
  three charges? (F net 118 N)

22
Problems

• The notation FBA is used to denote the force of B
  on A. 

23
Problems

• FBD (Free Body Diagrams)