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Eunil Won, Dept. of Physics, Korea Univ Ch10 Introduction to Electricity and Magnetism This is what it looks like inside your cellular phone : it is all about electricity and magnetism 1 Eunil Won, Dept. of Physics, Korea Univ Electric Charges and Forces Electromagnetism: the combination of electrical and magnetic phenomena Charges with the same electrical sign repel each other, and charges with opposite electrical signs attract each other conductors: some of electrons in materials can move rather freely ex) metals, human body insulators: none of electrons in materials can move freely ex) plastic, glass 2 Eunil Won, Dept. of Physics, Korea Univ Coulomb’s Law The electrostatic force of attraction or repulsion between two charged particles (q1 and q2) has the magnitude (Coulomb’s law) k: electrostatic constant Unit of charge: C (Coulomb) One Coulomb is the amount of charge that is transferred through the cross section of a wire in 1 second when there is a current of 1 Ampere 3 Eunil Won, Dept. of Physics, Korea Univ Coulomb’s Law k: electrostatic constant and is usually written as 1/4πε0 Then Coulomb’s law becomes ε0 permittivity constant: A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell’s charge were concentrated at its center If a charged particle is located inside a shell of uniform charge, there is no net electrostatic force on the particle from the shell 4 Eunil Won, Dept. of Physics, Korea Univ Charge is Quantized Benjamin Franklin thought that electric charge was a continuous fluid but... Experiments show that any charge q that can be detected written as: e, the elementary charge has the (small) value: Conservation of charge: the net charge of any isolated system cannot change 5 Eunil Won, Dept. of Physics, Korea Univ Electrostatic Force >> Gravitational Force FC = 10 Fg 39 FC = Fg = G 1 q p qe 4πε 0 r 2 mp me r2 −19 2 ( 1 . 60 × 10 ) −8 9 = 8 . 2 × 10 N = 8.99 ×10 −10 2 (0.53 ×10 ) −21 −27 ( 9 . 11 × 10 )( 1 . 67 × 10 ) −11 −47 = 6.67 ×10 = 3 . 6 × 10 N −10 2 (0.53×10 ) 6 Eunil Won, Dept. of Physics, Korea Univ Example 10.1 If all the positive and negative charges in 1 g of water could be separated, they would total 5.35 x 104 C and -5.35 x 104 C, respectively. Calculate the force between such charges when separated by 1.0 m. Negative sign: attractive force This is an extremely large force 7 Eunil Won, Dept. of Physics, Korea Univ The Electric Field We define the electric field at point due to the charged object: SI unit for the electric field: N/C (newton per Coulomb) Electric field lines: extend away from positive charge and toward negative charge 8 Eunil Won, Dept. of Physics, Korea Univ The Electric Field Due to a Point Charge The magnitude of the electrostatic force on q0 due to a point charge q: The magnitude of the electric field due to a point charge q: Net force from the n point charges: Net electric field due to n point charges: 9 Eunil Won, Dept. of Physics, Korea Univ The Electric Field Due to an Electric Dipole electric dipole: two charged particles of magnitude q but of opposite sign, separated by a distance d electric field at point P: note: p = qd : electric dipole 10 Eunil Won, Dept. of Physics, Korea Univ A Dipole in an Electric Field A molecule of water is an electric dipole: the electric dipole points from oxygen to the hydrogen side Let’s consider a dipole in an electric field (uniform): net force on the dipole is zero but there is torque acting on the dipole the magnitude of each force : F = qE assume x is the position of the center of mass of the dipole system: Generalizing the above we get: Note: torque is clockwise (reducing the angle θ) : we put minus sign with the torque (useful for the discussion with the potential energy) 11 Eunil Won, Dept. of Physics, Korea Univ A Dipole in an Electric Field Potential energy of an electric dipole at any angle θ: o (we choose the potential energy to be zero when the angle θ is 90 ) the integral becomes: or 12 Eunil Won, Dept. of Physics, Korea Univ Electric Potential Energy Newton’s law for the gravitation force and Coulomb’s law for the electrostatic force are mathematically identical The electrostatic force is also a conservative force : we can assign an electric potential energy U to the system (path independent) Convenience, we take U to be zero (all particles are infinitely apart each i other) 13 Eunil Won, Dept. of Physics, Korea Univ Electric Potential The potential energy per unit charge at a point : called the electric potential (V) (path independent) SI unit: J/C or 1 Volt (V) The electric potential difference between any two points i and f: ex) Home AC power has: 220 V We can now adopt a new unit for electric field: ex) energy required to move electron through 1 Volt potential difference: ex) energy required to move 1 kg by height of 1 m: 14 Eunil Won, Dept. of Physics, Korea Univ Equipotential Surfaces Adjacent points that have the same electric potential form an equipotential surface: no work is need for any path on the equipotential surface ex) equipotential surface for uniform electric field: plane equipotential surface produced by a point charge: concentric spheres 15 Eunil Won, Dept. of Physics, Korea Univ Calculating the Potential from the Field differential work done on a particle by a force (positive test charge q moves from i to f ): 0 the total work becomes: in other words: finally we choose the initial electric potential is zero 16 Eunil Won, Dept. of Physics, Korea Univ Potential Due to a Point Charge First we evaluate the dot product: the angle θ is zero (from the figure), and we take r=R from the initial and r=infinity to the final position we know that the integral becomes: note: positively charged particle produces a positive electric potential For a group of point charges: 17 Eunil Won, Dept. of Physics, Korea Univ Example 10.2 Calculate the speed of an electron accelerated by the 20,000 V potential difference found in the CRT. The mass of electron is 9.11x10-31 kg. KE = 12 mv 2 = qV 1/2 ⎛ 2(1.6 ×10 C)(2.0 ×10 V) ⎞ ⎛ 2qV ⎞ ⎟⎟ v=⎜ ⎟ = ⎜⎜ -31 9.11×10 kg ⎝ m ⎠ ⎠ ⎝ = (7.03 ×1015 m 2 /s 2 )1/2 = 8.4 ×107 m/s 1/2 -19 4 18 Eunil Won, Dept. of Physics, Korea Univ Definition of Current the free electrons in an isolated wire: in random 6 motion at speeds of 10 m/s but no net current through the wire when the wire is connected, there is a net transport of charge : electric current charge carrier: electron (but we define the direction of the current with +q) electric current: SI unit : 1 ampere = 1A = 1 coulomb per second = 1 C/s total charge passes through in a time interval electric charge conservation requires 19 Eunil Won, Dept. of Physics, Korea Univ Current Density current density: current per unit area with the direction defined by the current itself drift speed: electrons drift with a drift speed when there is a current in a conductor ex) vd ~ 10-5 or 10-4 m/s in copper conductors n : number of charge carriers per unit volume A : wire’s cross sectional area L : length of the wire under consideration Extending this as a vector form: For positive (negative) carrier, current density and the velocity have same (opposite) direction 20 Eunil Won, Dept. of Physics, Korea Univ Resistance and Resistivity We determine the electric resistance between any two points of a conductor by applying a potential difference SI unit: 1 ohm = 1 Ω = 1 volt per ampere = 1 V/A : a conductor provides a specified resistance is called a resistor resistivity: SI unit: in a vector form, conductivity: From the figure on the left: and : macroscopic quantities (practically useful) : microscopic quantities (useful in studying fundamental electrical properties of materials) 21 Eunil Won, Dept. of Physics, Korea Univ Ohm’s Law : an assertion that the current through a device is always directly proportional to the potential difference historically, it is called law but it is an (obeying Ohm’s law) assertion that may or may not be true Ohm’s law can be expressed as: or (I-V curve from a semiconducting pn junction diode) (microscopic) A Microscopic View of Ohm’s Law e: electric charge of an electron m: mass of electron E: electric field applied τ : average time between collisions From we get finally we get 22 Eunil Won, Dept. of Physics, Korea Univ 23 Eunil Won, Dept. of Physics, Korea Univ Example 10.3 How many electrons move through a pocket calculator during one hour of use? q = It q = (0.3 ×10 A)(1 hr) -3 = (0.3 ×10 C/s)(3600 s) = 1.08C -3 1 18 1.08C × = 6.75 ×10 -19 1.6 ×10 C 24