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From Last Time… Forces between charges Electric dipole 1 Exam 1 Wed. Feb. 20, 5:30-7 pm Covers Chap. 21.5-7, 22-23,25-26 + lecture, lab, discussion, HW 8 1/2 x 11 handwritten note sheet (both sides) allowed Students with schedule class conflicts: stay after lecture today to arrange time Review Group/Quiz (solutions on website). Review lab question sheets. Review sample exams on website. HW4 (due Fri. next week) covers exam material. 2 From Last Time… Forces between charges Electric dipole 3 Unusual dipoles: Electrogenic fish • Dipole + nearby conducting object Some fish generate charge separation - electric dipole. Dipole is induced in nearby (conducting) fish Small changes detected by fish. 4 The idea of electric fields • EM wave made up of oscillating electric and magnetic fields. • But what is an electric field? • Electric field is a way to describe the force on a charged particle due to other charges around it. • Force = charge electric field • The direction of the force is the direction of the electric field. 5 Electric field of a point charge Force on this charge… Q2 + + + Q1Q2 F k 2 rˆ r Q1 …due to this charge E F r /Q2 + = Force/unit charge Units? N/C 6 + Question Which vector best represents the electric field at the red dot? A B E C - D 7 Electric field • Electric field vector defined at every point in space. • Gives magnitude and direction of force on test particle e.g. wind velocity (speed and direction) in different parts of the country. 8 Relationship Between F and E • Fe = qE This is valid for a test charge small enough that it does not disturb the source charge distribution QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. • If q is positive, F and E are in the same direction Qp=1.6x10-19 C + Electric field 1Å away from proton E r= 9 2 19 9 10 N M /C 1.6 10 C 10 10 m 2 1x10-10 m E 2.9 1011 N /C (to the right) 9 Electric Field Direction • a) q is positive, F is • • • directed away from q b) The direction of E is also away from the positive source charge c) q is negative, F is directed toward q d) E is also toward the negative source charge 10 Superposition with Electric Fields • At any point P, the total electric field due to a group of source charges equals the vector sum of electric fields of all the charges Find the electric field due to q1, E1 Find the electric field due to q2, E2 E = E1 + E2 Remember, the fields add as vectors 11 Quick Quiz Which is the direction of the electric field at dot? A. Left B. Right C. Up Away from positive charge (right) D. Down E. Zero y + - x Net E field is to right. 12 Quick Quiz In this electric dipole, what is the direction of the electric field at point A? A) Up A B) Down C) Left D) Right x=-a +Q x=+a -Q E) Zero 13 Electric field: summary • Electric field -> will be a force on a charged particle. • This force ( and electric field) can arise from electric charges (via Coulomb’s law) • But once electric field is known, don’t need to know the charges that produce it. 14 Calculating dipole electric field y On the y-axis E E y yˆ E y E E kq kq 1 1 kq 2 2 y s /2 y s /2 + s/2 2ys 2 2 y s /2 y s /2 1 k 2qs 3 y For y s x - s/2 Since p points from - charge to + charge Ek 2p r3 on y-axis of dipole only 15 Question: electric dipole A and B are the same (large) distance from dipole. How do the magnitude of the electric fields at A and B compare? A) E A E B A B) E A E B C) E A E B B D) E B 0 16 Pictorial representation of E: Electric Field Lines 17 Electric field lines • Local electric field tangent to • • • • field line Density of lines proportional to electric field strength Fields lines can only start on + charge Can only end on - charge. Electric field lines can never cross 18 Point particles 19 Electric field of a dipole + - 20 Electric field of two + charges 21 Question How are the charges A and B related? A) A+, B-, A B B) A-, B+, A B C) A+, B-, A B D) A-, B+, A B A B E) A+, B-, A B 22 Hydrogen Atom Example • The magnitude of the electric force between the electron and • proton: Fe = ke|e| |-e| / r2 = 8.2 x 10-8 N, r ~ 0.53 x 10-10 m The gravitational force between the electron and the proton Fg = Gmemp / r2 = 3.6 x 10-47 N me = 9.11 x 10-31 kg, mp = 1.67 x 10-27 kg G = 6.67 x 10-11 N m2/kg2 Fe/Fg ~ 2 x 1039 Mp=1.67x10-27 kg Me = 9.11 x10-31 kg + r = 0.53x10-10 m 23