Electrostatics

1
Electrostatics
2
Learning Objectives

• The electrostatic force (Coulombs Law) can be
  either repulsive or attractive (SOL 12.a)
• The interaction of two particles can be described
  as the creation of a field by one of the
  particles and the interaction of the field with
  the second particle (SOL 12.b).

3

• Magnitude of charge on protons and electrons are
  exactly the same
• Protons have a positive charge
• Electrons have a negative charge
• Neutral atoms contain equal numbers of protons
  and electrons

4
Insulators and ConductorsNeed to know

• Insulator electrons are bound very tightly to
  the nuclei. Wood and rubber are good insulators.
• Conductor electrons are bound very loosely and
  can move about freely. They are often referred
  to free electrons. Metals are good conductors.
• Semiconductor very few free electrons (silicon,
  germanium and carbon)

5
Static Electricity

• You have probably experienced a charge lately
  (comb, dryer, carpet, car seat, )
• An object becomes charged due to a rubbing
  process and is said to possess a net electric
  charge
• An item containing a net positive charge has lost
  electrons
• An item containing a net negative charge has
  gained electrons

6
Law of Conservation of Electric ChargeNeed to
know

• The net amount of electric charge produced in any
  process is zero
• If one object or one region of space acquires a
  positive charge, then an equal amount of negative
  charge will be found in neighboring areas or
  objects

7
Unlike Charges AttractLike Charges RepelNeed
to know
8
3 Ways to Charge an ObjectNeed to know

1. Friction Rubbing two objects together with
   different electron attachment. Heat generated
   frees electrons to join object with stronger
   attachment.

9
3 Ways to Charge an ObjectNeed to know

• 2. Conduction Electrons are transferred from
  one object to another by touching. Usually it
  involves moving from one electric potential to
  another.
• John TraVOLTa Demo

10
3 Ways to Charge an ObjectNeed to know

• 3. Induction Rod does not touch sphere. It
  pushes electrons out of the back side of the
  sphere and down the wire to ground. The ground
  wire is disconnected to prevent the return of
  the electrons from ground, then the rod is
  removed.

11
Electromagnetism

• One of the four fundamental forces of the
  universe (electromagnetism, gravity, weak nuclear
  and strong nuclear forces)
• The forces that act between atoms and molecules
  to hold them together are electrical forces
• Elastic, normal and contact forces (pushes and
  pulls) result from electric forces acting at the
  atomic level

12
Forces resulting from charges

• Charges push and pull on one another
• Closer the charge the higher the force
• The stronger the charge the higher the force

13
Coulombs LawNeed to know

• The magnitude of the force between charge qA and
  charge qB, separated a distance d, is
  proportional to the magnitude of the charge and
  inversely proportional to the square of the
  distance
• F K qAqB
• d2

qA
qB
d
14
Coulombs Law Key FactsNeed to know

• The charge of an electron is
• -1.60 x 10-19 coulombs (C)
• The charge of a proton is
• 1.60 x 10-19 coulombs (C)
• The charge, q, is measured in coulombs. The
  distance, d, is measured in meters. The force,
  F, is measured in newtons.
• The constant, K 9.0 x 109 Nm2/C2

15
Problem Solving Strategy

1. Sketch the system showing all distances
2. Diagram the vectors
3. Use Coulombs law to find the magnitude of the
   force. Note it is unnecessary to include the
   sign of the charges or the distance. The answer
   is always positive.
4. Use your diagram along with trigonometric
   relations to find the direction of the force

16
Example Problem 1

• Two charges are separated by 3.0 cm. Object A
  has a charge of 6.0 ?C, while object B has a
  charge of 3.0 ?C. What is the force on object
  A?
• Known Unknown
• qA 6.0 x 10-6 C FB on A ?
• qB 3.0 x 10-6 C
• d 0.030 m

17
Example 1 Solution

• F K qAqB
• d2
• (9.0 x 109 Nm2/C2)(6.0 x 10-6C)(3.0 x 10-6C)
• (3.0 x 10-2 m)2
• FB on A 1.8 x 102 N

18
Example 2 Three Charges

• Given
• Find the net force on the -2 µC charge
• Known

19

• FA on B KqAqB
• d2
• (9x109 Nm2C2)(6x10-6 C)(2x10-6 C)
• (0.06 m)2
• - 30 N
• FC on B KqCqB
• d2
• (9x109 Nm2C2)(2x10-6 C)(2x10-6 C)
• (0.02 m)2
• 90
• FNet FA on B FC on B - 30 N 90 N 60 N

20
Example Problem 3

• A sphere with a charge 6.0 ?C is located near two
  other charged spheres. A -3.0 ?C is located 4.00
  cm to the right and a 1.5 ?C sphere is located
  3.00 cm directly underneath. Determine the net
  force on the 6.0 ?C sphere.

21
Example 3 Solution

• FB on A
• FC on A
• Fnet
• ??

22
Static Charge Generator
23
Electric Field Need to know

• An electric field extends outward from every
  charge and permeates all of space

24
Investigating the Electric Field

• We can quantify the strength of an electric field
  by measuring the force on a small positive test
  charge
• So small that the force it exerts does not
  significantly alter the distribution of the
  charges that create the field

a
25
Electric Field

• An electric field, E, at any point is defined as
  the force, F, exerted on a tiny positive test
  charge at that point divided by the magnitude of
  the test charge
• E F/qB

26
Electric Field Equation

• E F/qB
• E K qB qA/r2
• qB
• E KqA/r2

27
Example

• Calculate the magnitude and direction of the
  electric field at a point P which is 30 cm to the
  right of a point charge qA -3.0 x 10-6 C
• E KqA/r2
• Answer 3.0 x 105 N/C

28
Electric Field Lines

• Drawn so that they indicate the direction of the
  force due to the given field on a positive charge

29
Electric Field LinesNeed to KnowLines indicate
direction of the force due to the given field on
a positive test charge
30
Properties of Field LinesNeed to know

1. The field lines indicate the direction of the
   electric field
2. The lines are drawn so that the magnitude of the
   electric field, E, is proportional to the number
   of lines crossing unit area perpendicular to the
   lines. The closer the lines, the stronger the
   field.
3. Electric field lines start on positive charges
   and end on negative charges

31
Electric Potential DifferenceNeed to know

• V Won q PE Potential difference often q
  q referred to as Voltage
• Electric Potential Difference Units Volt J/C

g
E
displacement
displacement
W Fd mgd
W Vq

Big Negative Charge
32
Typical Voltages

• Source
• Thundercloud to ground
• High voltage power line
• Power supply for TV tube
• Auto ignition
• Household outlet
• Auto battery
• Resting potential across nerve membrane
• Potential changes on skin
• (EKG)

• Voltage
• 108 V
• 106 V
• 104 V
• 104 V
• 102 V
• 12 V
• 10-1 V
• 10-4 V

33
Example

• Two parallel plates are charged to a voltage of
  50V. If the separation between the plates is
  0.050 m, calculate the electric field between
  them.
• E V/d 50V/0.050m 1000V/m

- - - - -
E 1000 V/m
d 5 cm
34
Practice

• Two parallel plates are charged to a voltage of
  500V. If the separation between the plates is
  .0050 m, calculate the electric field between
  them.
• Two parallel plates are charged to a voltage of
  50V. If the electric field between them is
  10,000 V/m, what is distance between the plates?
• Answers
• 100,000 V/m
• .0050 m

35
CapacitorsNeed to Know

• A capacitor is a device that can store electric
  charge
• Consists of two conducting objects placed near
  each other but not touching
• They store charge for later use
• Usage camera flash, energy back-up for computers
  and as surge protectors

36
Capacitors

• Consists of a pair of parallel plates of area, A,
  and separated by a small distance d.
• In a diagram, they are represented by the symbol
• If a voltage is applied to a capacitor, one plate
  acquires a negative charge and the other an equal
  amount of positive charge.

37
CapacitorsNeed to Know

• The amount of charge acquired by each plate is
  proportional to the potential difference
• Q CV
• Where C is constant and is called the capacitance
  of the capacitor
• Unit Coulombs/Volt Farad
• Typical capacitor range is 1pF (10-12) to 1?F
  (10-6)

38
Determining Capacitance

• Constant for a given a capacitor
• Depends on structure and dimensions of he
  capacitor itself
• C ?o A/d
• A area
• d separation distance between plates
• ?o 8.85 x 10-12 C2/Nm2
• permittivity of free space