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Lecture 3.7 ELECTRICITY Electric charge Coulomb’s law Electric field ELECTRICITY Interaction between electrically charges objects Many important uses Light Heat Rail travel Computers Central nervous system Human body made up of electric charges. Atoms contain positive and negative charges Atoms bound together by electric forces » molecules Molecules interact to produce bones, blood, skin, etc ELECTRICITY Historical 6th century B.C., Greeks noticed sparks were produced when the fossilized tree resin called amber was rubbed with fur. Greek word for amber is elektron from which the word electricity is derived. Major discovery 1861: Maxwell’s equations. Unified electric and magnetic phenomena (electromagnetism). End of the 19th and early 20th century: Fundamental discoveries concerning the electronic structure of the atom were made. Electric charge and the atom Electric charge is a characteristic of subatomic particles. Simple View An atom is composed of 3 kinds of particles: protons , electrons and neutrons. Atom Nucleus Neutrons Protons e e e Particle Charge Value (SI unit) proton +e 1.6 x 10-19 Coulomb (C) electron -e -1.6 x 10-19 Coulomb (C) neutron none ----------------- Electric charge and the atom Carbon Atom Nucleus - 6 protons: charge +6e 6 neutrons: (no charge) - - 6 electrons: charge -6e - Atoms are electrically neutral Total positive charge of the nucleus = total negative charge of the electrons around the nucleus. These particles are, in general, neither created nor destroyed, but electrons can be displaced from one atom to an other. Electron removed – result positive ion Electron added – result negative ion Electric charge and the atom Electric charge is a basic physical property of subatomic particles, protons and electrons. 3 Properties of charge 1. Two types of charges, positive and negative 2. Charge is conserved. Cannot be created or destroyed. Charges can be separated. 3. Like charges repel and unlike changes attract Electrostatic forces result from the separation of positive and negative charges. Electric charge Electrically charged materials Many examples Almost any two non-conducting substances when rubbed together will become charged Plastic comb run through your hair comb will then attract bits of paper Balloon and wool rubbed together: balloon becomes - negatively charged -- -- + + + + + + - Friction associated with rubbing does not create the charge Charge transferred by movement of electrons Charge is conserved Neither created or destroyed Total amount of charge in universe: constant Electric charge Basic unit of positive charge: +e = 1.6 x 10-19 Coulomb Basic unit of negative charge: -e = -1.6 x 10-19 Coulomb (C) Any charged object: •Total charge is always a multiple of e •Charge can only have values ±e, ±2e, ±3e ±.. •Charge is said to be quantised •Never fractional charge Coulomb’s Law Fundamental quantity of charge found in matter is that associated with a proton (+e) and electron (-e) Example. How many electrons are required to make up a negative charge of one Coulomb? Charge on an electron = -1.6x10-19C -1C therefore -1.6x10-19C = 6.25x1018 electrons are required to make up a charge of 1 Coulomb. Electric charge Types of Materials Conductors•Example: metals, copper etc. •charges are free to move. Insulators•Example: Rubber, plastic etc •charges are not free to move. Semiconductors• Example: Silicon, Germanium •movement of charges can be controlled by temperature or doping of the material. Application: electronic devices Photoconductors: •Example: Selenium •In darkness: Insulator •Exposed to light: conductor •Application: photocopier, laser printer Electric charges and forces Coulomb’s law Mathematical law that describes how •like charges repel •unlike charges attract Charles Coulomb (1736-1806) French physicist, Unlike charges q1 F + F -q2 Like charges q2 q1 F F - r q1q2 F∝ 2 r r q2 F + q1 F + r Coulomb’s law: “the force between two point charges is proportional to the product of their charge and inversely proportional to the square of their separation” Direction of the force: along line joining the point charges. Coulomb’s Law q1q2 F∝ 2 r q1q2 F =k 2 r SI unit of charge is called the Coulomb Force F is known as the Coulomb force or electrostatic force and its units are Newtons distance r is in metres Hence units of k are Nm2C-2 The constant k is determined by experiment to be 9x109 Nm2C-2 (in a vacuum) The constant k is frequently written as k= 1 4πε 0 where ε0 is called the permittivity of free space ε 0 8.85 ×10−12 C 2 N −1m −2 = Coulomb is a very large quantity of charge Coulomb’s Law Example: Two charges, each of one Coulomb, are a distance of 1 metre apart. What is the force between them? 1C∗ 1C 1 q1q2 F= 2 = 4π 8.85x10-12C2N-1m-2 ∗1m∗1m 4πε 0 r F = 9x109 N = 9 billion Newtons Coulomb force is very large compared with gravitational force Coulomb Force Example Compare electrostatic repulsive force between two electrons held one metre apart in a vacuum and the gravitational force of attraction between them? e = 8.85 × 10-12 C2N-1 m-2 0 mass of an electron = 9.11 × 10-31 kg G = 6.67 × 10-11 N m2 kg-2 1 q1q2 F= 4πε 0 r 2 Coulomb force 1.6 x10-19C∗ 1.6x10-19C F= 4π 8.85x10-12C2N-1m-2 ∗1m∗1m F = 2.3 x 10-28 N Gravitational force F= 6.67 ×10 −11 m1m2 F =G 2 r ( 9.11×10 ) −31 2 12 F = 5.5 x 10-71 N Coulomb’s Law Electron and proton, a distance r apart, are simultaneously released from rest. Where do they collide? -F + F Proton q =+e r Electron q= -e Newton 3rd law, forces are equal and opposite Collision at midpoint ?? acceleration F a= m Newton 2nd law F = ma electron mass = 9.11 × 10-31 kg proton mass = 1.67 × 10-27 kg Mass of proton ≈ 1833 times mass of electron acceleration of electron 1833 times greater Coulomb’s Law 1 2 = x v0t + at 2 xe ae = xp ap xe xp 1 2 xe = aet 2 1 2 x p = a pt 2 xe F / me m p = = x p F / m p me 1.67 ×10-27 kg 1833 = -31 9.11×10 kg 1 xe = 1833 x p + r Collide very near initial position of proton Electric Field Electrostatic force and gravitational force can both act through space even when there is no physical contact between the objects involved. Gravitational field: g m mass m experiences a force: F = mg Potential Energy ∆U ≈ mgh Field lines show the direction of the force and indicate its relative magnitude In the case of charged particles, what transmits the force between them? An electric field exists in a region of space around a charged object. Electric Field Electric field lines + - Electric field near a negative charge is directed radially into the charge as shown 2+ Electric field near a positive charge is directed radially out from the charge Double the charge Double the number of field lines Similar to gravitational field lines Electric field lines show • direction of the force • indicate its relative magnitude Electric Field Consider positive test charge q0(fictitious) at A Test charge: helpful in determining forces generated by other charges Assume test charge is small and does not affect any other charges Consider force on positive test charge q0 +A - q0 +A + Electric field represents the electric force a stationary positive charge experiences. Electric Field The electric field E is said to exist in the region of space around a charged object. Example: Q +++ + + +++ + ++ + Test charge q0 + F is the force exerted on q0 by Q Electric field E due to charge Q at location of small test charge q0 is given by; F E= q0 Electric force per Coulomb SI unit of electric field Newton per coulomb (NC-1) Electric Field F E= q0 F = q0 E Analogous to F= mg in gravitational field 1 Qq0 F = 2 4πε 0 r = Eq0 1 Q E = 2 4πε 0 r Electric field at a given point depends only on the charge Q on the object setting up the field and the distance r from the object to the specific point in space Electric Field Example Determine the electric field at A, a distance of 40cm from a positive charge Q of 2x10-3 Coulombs Q A E + r Find field E at point A 40 cm from Q. Q E=k 2 r -3) C (2 x 10 E= 9 x 109 N.m2C-2 (0.4m)2 E = 112.5 x106 NC-1 Electric charges Example How many electrons must be removed from an object so that it is left with a charge of 8 x10-10 C Total charge = 8 x 10-10 C Charge on electron = -1.6 x 10-19 C Therefore number of electrons removed = 8 x 10-10 C 1.6 x 10-19 C = 5 x 109 electrons Coulomb force Example Determine the minimum distance apart two identical charges of 0.1 C must be in order that the Coulomb force between them is less than 500 N. k = (9 x 109) Nm2C-2 q1q2 F =k 2 r 9 ×109 Nm 2C −2 ( 0.1C × 0.1C ) 500 N r2 9 9 × 10 0.1× 0.1) ( 2 r 500 9 ×109 ( 0.1× 0.1) r 500 r 420m Electric charges Example An object has a total charge of -2 x10-6 C. How many excess electrons does the object have. Total charge = -2 x 10-6 C Charge on electron = -1.6 x 10-19 C Therefore number of excess electrons = -2 x 10-6 C -1.6 x 10-19 C = 1.25 x 1013 electrons