Charges, voltage and current Lecture 2 1 Atoms and electrons Atoms are built up from Positively charged nucleus Negatively charged electrons orbiting in shells (or more accurately clouds or orbitals) - - + Negative charge = positive charge so atoms are NEUTRAL Lecture 2 2 1
Electric charge Electric charge is measured in Coulombs (symbol C) The charge on the electron is - 1.621892 x 1-19 C The charge on the proton is +1.621892 x 1-19 C usually referred to as e This is a fundamental constant of our universe The symbol that we use for charge in equations is usually Q or q Charles Augustin de Coulomb (1736 186) Published the inverse square law of electrical attraction Lecture 2 3 Free charges We can remove electrons from (some) atoms quite easily Heating Electrical sparks Friction Photo-electric effect Separated electric charges have a very strong force between them (the electrostatic force) + + Like charges repel Opposite charges attract - + The force obeys the inverse square law The positively charged atom left behind is called an ion Lecture 2 4 2
Inverse square law F q 1 r + + -q 1 - + +q 2 F F F = q q 1 2 2 r 4πε q 2 F Units: Newtons when charges are in coulombs and distance in metres ε (epsilon nought) is called the permittivity of free space and is another fundamental constant of our universe which relates electrostatic effects to force (and so to energy) ε = 8.854188 x 1-12 C 2 N -1 m -2 Lecture 2 5 Inverse square law F -q 1 q 1 q 2 r + + - + +q 2 F F F F = q q 1 2 2 r 4πε The force between two charges of 1 C separated by 1 metre: 1 F = Newtons 4πε approximately 9,,, N or 916, tonnes!! The electrostatic force is by far the strongest physical force that we normally experience and is responsible for all of the macroscopic properties of matter Lecture 2 6 3
Electric field The electrostatic force can be expressed in terms of ELECTRIC FIELD (symbol E) A vector field surrounding charges with magnitude proportional to the force on a point charge direction in the direction of the force on a positive charge (i.e. electric field arrows point towards NEGATIVE charges) F = qe (units of E for now, N C -1 ) Lecture 2 7 Electric field surrounding point charges E + - Er () q = 4πε r 2 Lecture 2 8 4
Moving electrons A free electron in an electrostatic field experiences a force and so it accelerates and gains kinetic energy. The further it moves through the field, the more energy it gains. v= - F v - F E d Lecture 2 9 Moving electrons v= - F v - F E d In a uniform field, force is constant, so velocity increases like 2 2Eqd v = m 1 2 mv = Eqd 2 The electron kinetic energy increases linearly with distance along the electric field Electronics is all about exploiting energetic electrons Lecture 2 1 5
Direct application of fast electrons the cathode ray tube Colour TV or monitor tube A. Electron gun B. Glass vacuum envelope C. Beam deflection and focusing F. Phosphor screen Small CRT e.g. for an oscilloscope Carbon nanotubes for a modern Field-Emission Display Lecture 2 11 Potential differences THE VOLT K.E. + + + + P.E. 5 J 1 J 2 J 3 J 4 J + Q=1 C 4 J 3 J 2 J 1 J E 5 J - - - - - P.D. 5 V 4 V 3 V 2 V 1 V A charge in an electric field has POTENTIAL ENERGY As it moves through the field it gains KINETIC ENERGY The increase in K.E. for a charge of 1 C is called the POTENTIAL DIFFERENCE or ELECTROMOTIVE FORCE (e.m.f.) This is such an important parameter that it has its own unit the VOLT (derived from J C -1 ) Lecture 2 12 6
THE VOLT (symbol V) A potential difference of 1 volt will give 1 joule of kinetic energy to a charge of 1 coulomb Energy = QV Alessandro Volta (1745-1827) Credited with constructing the first chemical battery Lecture 2 13 A demonstration Voltaic pile from ~1825 Two dry piles, insulated with sulphur - + The metal ball suspended on a silk thread alternately charges + and and oscillates between the bells Claimed to be the world s most durable battery (Guinness Book of Records) or (popularly) a perpetual motion machine! + + - - Clarendon Laboratory Museum, Oxford Lecture 2 14 7
An analogy P.E. = mgh who? K.E. 1 J 2 J + + + + + Q=1 C F=EQ P.E. 5 J 4 J 3 J P.D. 5 V 4 V 3 V 3 J 2 J 2 V F=mg 4 J 1 J 5 J E - - - - - 1 V K.E. = ½mv 2 A charged particle moving in an electric field has exactly the same dynamics as a mass falling under gravity Lecture 2 15 A new definition for electric field We can now define electric field in terms of VOLTAGE Remember that Field is Force per unit charge (newtons per coulomb) Voltage is energy per unit charge (joules per coulomb) Energy is Force x Distance (joules = newton.metres) so Voltage = Field x distance Field = Voltage / distance: Units V m -1 l +V E=V/l In a uniform field, E=-V/l, V=-El In a non-uniform field, dv El () = dl l V = E() l dl Lecture 2 16 8
Current Moving charged particles transport charge from one point to another The rate of charge transport across any surface is called the CURRENT [symbol in equations i or I, unit Ampères (A)] If N particles of charge q cross a surface in time t, the current is given by i = Nq t Ampères The early experimenters got it wrong. Current is carried by electrons and so we have to remember that current flow is OPPOSITE to electron flow. Electrons: Negative to Positive Current: Positive to Negative Lecture 2 17 Statue in Lyon André-Marie Ampère (1775-1836) Investigated the magnetic effects of electric currents Lecture 2 18 9
Current and charge In practice, the flow of charge carrying particles is not constant with time so we have to use a differential definition for the instantaneous current at a particular time t: dq it () = dt where dq is the small amount of charge (C) which flows in the small time from t to t+dt (sec). To get the total charge that has flowed in a particular time period we need to integrate the current: t 2 Q= i() t dt t1 If current is constant, charge=current x time current = charge/time Lecture 2 19 Current flow and power Moving electrons carry ENERGY as well as charge, and so an electric current has POWER (rate of arrival of energy) [symbol in equations P, unit Watt = 1 Joule per second, W] Similarly to current we can define the power as Pt () = de dt where de is the small amount of energy crossing our surface between t and t+dt We already know that the energy of a particle of charge q coulombs with voltage V volts is qv joules, so Pt () Vit () = watts = volts x amps Lecture 2 2 1
James Watt (1736-1819) Scottish engineer most famous for the development of steam power he was the first to use the term horse-power Lecture 2 21 Active and passive components +V I +V I W W Passive: Current flow is in the direction of the voltage (+ to -) Power is absorbed from the current by the components and transferred to the surroundings Active: Current flow is in the OPPOSITE direction to the voltage (- to +) Power is absorbed from the surrounding by the components and transferred to the current flow Lecture 2 22 11