Transcript Electricity and Magnetism - Floyd County High School

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.
Electric Charges
• Evidence for electric charges is everywhere, e.g.
– static electricity.
– lightning.
• Objects may become charged by contact and
frictional forces.
• Benjamin Franklin (1700’s) 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)
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)
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).
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)
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).
Electric Force and Coulomb’s Law
• If two point charges q1 and q2 are separated
by a distance r, the magnitude of the electric
force Fe between them is:
Fe  k
q1 q2
r
2
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).
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.
Electric Force Vector
• The force on a point charge q1 exerted
by another point charge q2 separated
by a distance r21 is:



kq1q2
F12  2 rˆ21
F21   F12
r21
where rˆ21 is a unit vector along theaxis
joiningq2 and q1.
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:
 


F1  F12  F13   F1N
• Each charge may be considered to exert a
force on q1 that is independent of the other
charges present.
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 :

 Fe
E
in N/C
q0
Electric Field
• The electric force on a positive test charge q0
at a distance r from a single charge q:

qq 0
Fe  k 2 rˆ
r
• The electric field at a distance r from a single
charge q:

 Fe
q
E
 k 2 rˆ
q0
r


Fe  q0 E
Electric Field due to
a Group of Charges:

qi
E  k  2 rˆi
r
i
i
rˆi is a unit vector from qi to q0
Example Problem
Four point charges are at
the corners of a square
of side a as shown.
a) Determine the
magnitude and direction
of the electric field at
the location of q.
b) What is the resultant
force on q?
2q
a
q
a
3q
a
a
4q
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:
dQ
dQ
dE  k 2
E   dE  k  2
r
r

dQ
1
dQ
1
E  k  2 rˆ 
rˆ k 
2

r
4 0 r
4πε0
ε0 = permittivity of free space
Uniform Charge Distributions
ρ=Q/V
• Surface Charge Density: σ=Q/A
• Linear Charge Density:
λ=Q/l
• Volume Charge Density:
Example:
• A continuous line of charge lies along the xaxis, extending from x=x0 to positive infinity.
The line carries a uniform linear charge
density λ0. What are the magnitude and
direction of the electric field at the origin?
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 λo. 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?
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.
Electric Field Lines: Conventions
Positive Point Charge
Negative Point Charge
Electric Field lines