Download Week3-Week4. - WordPress.com

Int. to Electrical-Electronics
Engineering
Asst. Prof. Dr. Alper ŞİŞMAN
Fund. Physics Law in EE
• Physical laws
– Coulomb's law
– Gauss's law
– Ampère's law
– Ohm's law
– Faraday's law of induction/Farady-Lenz law
– Kirchhoff's circuit laws
• Current law
• Voltage law
Coulomb’s Law
• Describes the electrostatic interaction between
electrically charged particles
• Essential to the development of the theory of
electromagnetism
• It is analogous to Newton's inverse-square law of
universal gravitation.
• The magnitude of the electrostatic force of interaction
between two point charges is directly proportional to
the scalar multiplication of the magnitudes of charges
and inversely proportional to the square of the
distances between them.
• If the two charges have the same sign, the electrostatic
force between them is repulsive; if they have different
sign, the force between them is attractive.
• Coulomb's law can also be stated by the
following mathematical expression:
• Here q1 and q2 are point
charges, r21 is the distance between them,
r21 vector is the distance vector that has the
direction depends on the charge signs and ke is
the Coulomb's constant is given by 1 / (4πε)
where ε is the permittivity of the material in
which the charges are immersed.
Electric Field
• An electric field is a vector field that associates
to each point in space the Coulomb force
experienced by a test charge.
• The test charge (qt) has 1 Coulomb charge
value=>
• Vector fields?
Gauss Law
• Gauss's law, also known as Gauss's flux
theorem, is a law relating the distribution of
electric charge to the resulting electric field
•
Here phi is the the electric flux
through a closed surface S, Q is total charge
inside the volume bounded by the surface.
• The rlrctric flux canbe defined by the following
surface integral:
Amperes Law
• It relates magnetic fields to electric currents that
produce them.
• Using Ampere's law, one can determine
the magnetic field associated with a
given current or current associated with a given
magnetic field, providing there is no time changing
electric field present.
• In terms of total current, which includes both free
and bound current, the line integral of the
magnetic B-field (in tesla, T) around closed curve
C is proportional to the total current passing
through a surface S (enclosed by C):
• Mathematical expression for amperes law:
• Here, is the closed line integral around the
closed curve C, B is the magnetic field (Tesla),
Ienc is the enclosed current and µ0 is the
magnetic permeability of the ambient.
• See the analogy between gauss and amperes
laws
Ohms Law
• What is potential?
– The potantial of a point is defined : as the
required energy to bring the unity charge from
infinity to that point in an electric field.
– dW=F*dr=> dW = qEdr, Here q is unity! =>
– dW = ((1/4πε)*q/r2)dr=> V=W=∫((1/4πε)*q/r2)dr
and the limits of integration are: r……infinite
Thus the result: V=((1/4πε)*q/r)dr.
– Electric potential is a scalar quantity while electric
field is defined as a vector.
Ohms Law
• Ohm's law states that the current through a
conductor between two points is directly
proportional to the potential difference across
the two points.
• What is voltage difference
• What is current
• Current density J=I/A
• Electric field-current density relation: J=E*sigma,
E=J*rho
• Electric field voltage relation V=E*L
• V=I*(rho* L/A). Here rho L/A is resistance (R) and
V=IR
Faraday's law of induction
• Electromagnetic induction is the production of a
potential difference (voltage) across a conductor
when it is exposed to a varying magnetic field.
• Faraday's law of induction is a basic law of
electromagnetism predicting how a magnetic field
will interact with an electric circuit to produce an
electromotive force (EMF). It is the fundamental
operating principle of transformers, inductors, and
many types of electrical motors, generators and
solenoids.
diagram of Faraday's
iron ring apparatus:
• When the flux changes—because B changes,
or because the wire loop is moved or
deformed, or both—Faraday's law of
induction says that the wire loop acquires an
EMF, defined as the energy available from a
unit charge that has travelled once around the
wire loop:
• and, EMF:
• Here v is the relative velocity, B: magnetic field, E:
Electric field, dl: the integration over the wire and q:
the total charge of the particule (electron).
Kirchhoff's circuit laws
• Kirchhoff's circuit laws are two approximate
equalities that deal with the current and potential
difference (commonly known as voltage) in electrical
circuits. They were first described in 1845 by Gustav
Kirchhoff. This generalized the work of Georg Ohm
and preceded the work of Maxwell.
• Kirshoff current law, the principle of conservation of
electric charge implies that: At any node (junction) in
an electrical circuit, the sum of
currents flowing into that node
is equal to the sum of currents
flowing out of that node.
• Kirshoff voltage law: This law is based on one of the
Maxwell equations, namely the Maxwell-Faraday law
of induction, which states that the voltage drop
around any closed loop is equal to the rate-of-change
of the flux threading the loop.