Electricity and Magnetism

1
Electricity and Magnetism

• Electric forces hold atoms and
  molecules together.
• Electricity controls our thinking, feeling,
  muscles and metabolic processes.
• Electricity and magnetism underpin much of our
  current technology (e.g. computers).
• Electricity and magnetism are linked on a
  fundamental level.

2
Electric Charges

• Evidence for electric charges is everywhere, e.g.
• static electricity.
• lightning.
• Objects may become charged by contact and
  frictional forces.
• Benjamin Franklin (1700s) discovered that there
  are two types of charges
• positive charge.
• negative charge.
• Franklin also discovered that like charges repel
  and unlike charges attract one another.
• Electric charge is
• quantized (Millikan)
• conserved (Franklin)

3
Electric Charges in Atoms

• Atoms consist of a nucleus containing positively
  charged protons.
• The nucleus of an atom is surrounded by an equal
  number of negatively charged electrons.
• The net charge on an atom is zero.
• An atom may gain or lose electrons, becoming an
  ion with a net negative or positive charge.
• Polar molecules have zero net charge but their
  charges are unevenly distributed in space (e.g.
  water).

Nuclear diameter 10-15 m
(femtometer) Atomic diameter 10-9 m
(nanometer)
4
Classes of Materials

• CONDUCTORS are materials in which charges may
  move freely (e.g. copper).
• INSULATORS are materials in which charges cannot
  move freely (e.g. glass).
• SEMICONDUCTORS are materials in which charges may
  move under some conditions (e.g. silicon).

5
Charges and the Earth

• The earth acts as a near-infinite source or sink
  of charges, and therefore its net charge cannot
  easily be changed.
• Any conductor in contact with the earth is said
  to be GROUNDED and cannot receive a net charge.
  (principle of lightning rod)

6
Induced Charge

• Charged objects brought close to a conductor may
  cause charge to redistribute (polarize the
  conductor).
• If a polarized conductor is momentarily grounded,
  charge will be transferred to/from the earth, and
  it may be left with a net charge (by INDUCTION).
• Objects may be charged by
• conduction (requires contact with another charged
  object.
• induction (requires no contact with another
  charged object).

7
Electric Force and Coulombs Law

• If two point charges q1 and q2 are separated by a
  distance r, the magnitude of the electric force
  Fe between them is

where k 8.99 x 10 9 N? m2/C2 is the Coulomb
constant, q1 and q2 are in Coulombs (C), r is in
meters (m) and Fe is in Newtons (N).
8
Quantum of Electric Charge

• Electric charge is quantized. The smallest
  possible unit is the charge on one electron or
  one proton
• ?e? 1.602 x 10-19 Coulombs
• No smaller charge has ever been detected in an
  experiment.

9
Electric Force Vector

• The force on a point charge q1 exerted by
  another point charge q2 separated by a distance
  r21 is

10
Principle of Superposition

• For a system of N charges q1, q2, q3, , qN, the
  resultant force F1 on q1 exerted by charges q2,
  q3, , qN is

• Each charge may be considered to exert a force on
  q1 that is independent of the other charges
  present.

11
Field Forces and Electric Field

• Field forces act through space even if there is
  no contact (e.g. gravitational force).
• The ELECTRIC FIELD E is defined in terms of the
  electric force that would act on a positive test
  charge q0

12
Electric Field

• The electric force on a positive test charge q0
  at a distance r from a single charge q

• The electric field at a distance r from a single
  charge q

13
Electric Field due to a Group of Charges
14
Example Problem

• Four point charges are at the corners of a square
  of side a as shown.
• Determine the magnitude and direction of the
  electric field at the location of q.
• What is the resultant force on q?

q
2q
a
a
a
a
4q
3q
15
Electric Field from Continuous Charge
Distributions

• If a total charge Q is distributed continuously,
  it may be sub-divided into elemental charges dQ,
  each producing an electric field dE

e0 permittivity of free space
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Uniform Charge Distributions

• Volume Charge Density ?Q/V
• Surface Charge Density sQ/A
• Linear Charge Density ?Q/l

• Example
• A continuous line of charge lies along the
  x-axis, extending from xx0 to positive infinity.
  The line carries a uniform linear charge density
  ?0. What are the magnitude and direction of the
  electric field at the origin?

17
Example Problem Electric Field due to a Power
Line

• A power line is suspended a constant distance yo
  above the ground, and carries a uniform linear
  charge density ?o. Assume that the wire is
  infinitely long and that the ground is a flat
  plane. What are the magnitude and direction of
  the electric field on the ground immediately
  below the power line?

18
Electric Field Lines

• Electric Field Lines
• describe the direction of the electric field at
  any point
• The density of field lines is proportional to the
  magnitude of the electric field.
• The directions of arrows indicate the direction
  of the force on a positive test charge.
• Rules
• Lines begin on charge and end on charge
• Number of lines approaching or leaving a charge
  is proportional to the magnitude of the charge.
• Electric field lines may never cross.

19
Electric Field Lines Conventions
Positive Point Charge Negative Point
Charge
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Electric Field lines