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Physics 202, Lecture 2 Today’s Today s Topics Electric Force and Electric Fields Electric Charges and Electric Forces Coulomb's Law Physical Field The Electric Field Electric Field Lines Motion M ti off Charged Ch d Particle P ti l in i Electric El t i Field Fi ld A Reminder Lectures supplement but do not substitute for reading ! Lecture Effectiveness = Preview + Lectures + Review Properties of Electric Charges 2+1 types: positive, negative (+neutral). Unit: Coulomb (C). 1 C= charge of 6.24x1018 protons. 19 C El Electric i charge h is i quantized: i d q=±Ne, N e=1.602x10 1 602 10-19 Building blocks of matters: Charge (C) Electron Proton Neutron -e=-1.602x10-19 +e=+1 +e +1.602x10 602x10-19 0 Mass (kg) 9.11x10-31 1 673x10-27 1.673x10 1.675x10-27 Electric charge is conserved: charges can be moved around, but the total charge remains the same. For deep thinkers: Why electrons and protons have th same electric the l t i charge? h ? Electric Force And Coulomb’s Law Electric forces exist between two charged particles The direction of electric force depends on the signs of the charges: forces between opposite sign charges are attractive forces between like sign g charges g are repulsive p + - - + + + - - The Th magnitude it d off the th electric l t i forces f for f point i t charges h q1 q2 F12 = F21 = ke 2 r (Coulomb’s (Coulomb s Law) Coulomb Constant: ke = 8.987x109Nm2/C2 = 1/(4πε0) ε0: permitivity of free space Numeric Examples: Electric Force Is Huge Electric force between two 1C charges 1 meter apart: F=8.99x109N Proton and electron in a hydrogen atom: qelectron= -1.6x10-19 C, qproton= 1.6x10-19 C, r=5.3x10-11m Æ Electric force F= 8 8.2 2 x10-8 N. N ¾ This force is huge: Compared to the mass of proton: 1.673x10 1 673x10-27 kg Compared to the gravitational forces between them: FG= 3.6x10-47N ((recall: FG=Gm1m2/r2) Four fundamental forces: Strong > Electromagnetic > Weak >> Gravitational Coulomb’s Law in Vector Form r q1q2 E. Force on q2 by q1: F12 = Ke 2 r̂12 r r r q1q2 E. Force on q1 by q2: F21 = Ke 2 rˆ21 = −F12 r Exercise: Use this vector form to verify the attractive/repulsive feature Note: Multiple particles on charge i, Fi= F1i+F2i+ F3i +…. r r̂12 Exercise: Electric Forces Due to Two Charged g Particles Find the electric force on q3. Solution: See board. board Properties of the Electric Force It is one of four fundamental forces: Strong >Electromagnetic > weak >> gravity It is proportional to 1/r2 : double r Æ ¼ F Its direction is charge sign dependent: like signÆ repulsive, opposite sign Æ attractive It is a conservative force. (Work independent of path) W =∫ rf ri r r ke q1q2 ke q1q2 F • dr = − + = ( −U f ) − ( −U i ) rf ri ÎA potential energy can be defined. (Ch. 25) ke q1q2 U= r A Very Important Concept: Field What is a “field” ? Field: A physical quantity which has a physical value* at each point in space (i.e. a distribution). Examples of physical fields: temperature, p , wind speed, p , electric field,, magnetic g field,, … In this course, we consider only scalar and vector physical quantities. Example of Scalar and Vector Fields Temperature (scalar) Wind speed (vector) Measurement can be made at any point on the map. The Coulomb’s Law Revisited Original (Coulomb’s) view of electric force: q1 directly applies an electric force on q2 r q1q2 F12 = Ke 2 r̂12 r “Modern” view of electric force: q1 creates an electric field E around it The electric field E applies a force on q2 r r q1 F2 = Ke 2 rˆ12 q2 = E q2 r E In this modern view: q1: source charge q2: test charge E independent of q2! Electric Field and Electric Force r r q0 F = E q = Ke 2 rˆ q q r q0 E = Ke 2 rˆ r q0 q0: source charge E: field by q0 q: test charge F = qE E force f on q b by E 12 Visualization of Electric Field: Field Lines Use of field lines is a convenient way to visualize electric fields Simple rules for drawing field lines: line direction direction: direction of E vector ector line density: relative strength of E. (denser = larger) Field Lines e.g.: Point-Like Charges Magnitude E=ke q/r2 + +q Magnitude E=ke q/r2 -q q Example 2: Two Charged Particles + and +q d +q + + and +q d - q (dipole) (di l ) Each field line always starts from a + q and end at a -q (or ∞) Motion Of Charged Particle In The Electric Field Fundamental Formulas: F=qE a=F/m = qE/m v= vi +at If initially rest (vi =0) th then v= att = (qE/m) ( E/ ) t Motion of +q: Same dir. dir as E +q -q E Motion of - q: Opposite dir dir. as E 16 Exercise: An Electron in a Uniform E. Field Find out vertical displacement after the electron pass through a downward uniform electric field E Solution: Exercise with your TAs Answer: dy= - ½ (e/m)E (l/vi)2 17 Cathode Ray Tube (CRT) 18