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 fluxthrough 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……infiniteThus 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.