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## From Last Time…

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**+**+ From Last Time… Magnitude of the electric force Direction of the electric force**Induced dipoles (charge redistribution)**charged rubber rod Bring negative charge close. Electrons on sphere move away from rod.**Exam 1**Tue. Sep. 29, 5:30-7 pm, 145 Birge Covers Chap. 21.5-7, 22, 23.1-4, 23.7, 24.1-5, 26 + lecture, lab, discussion, HW 8 1/2 x 11 handwritten note sheet (both sides) allowed • Study ideas: • Exam 1 Practice problems at Mastering Physics • Sample exams on website (blank & solutions) • Group/Quiz (blank & solutions). • Review lab question sheets. 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.**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.**+**+ + + Q2 + Q1 Electric field of a point charge Force on this charge… …due to this charge = Force/charge Units? N/C**+**Calculating the electric field r = 10 cm Q1=1µC**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.**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**Question**Which vector best represents the electric field at the red dot? A B E C D - -**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**Qp=1.6x10-19 C**+ r = 1x10-10 m Relationship Between F and E • Fe = qE • Valid for a test charge that does not disturb the source charge distribution • If q is positive, F and E are in the same direction Electric field 1Å away from proton E (to the right)**Quick Quiz**Which is the direction of the electric field at dot? A. Left B. Right C. Up D. Down E. Zero Away from positive charge (right) y + - x Net E field is to right.**Quick Quiz**In this electric dipole, what is the direction of the electric field at point A? Up Down C) Left D) Right E) Zero A x=-a x=+a +Q -Q**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.**The electric dipole**• Can all be approximated by electric dipole. • Two opposite charges magnitude qseparated by distance s Dipole moment Vector Points from - charge to + charge Has magnitude qs**For**Since points from - charge to + charge on y-axis of dipole only Calculating dipole electric field y On the y-axis q s x -q**A**B 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?**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**+**- Electric field of a dipole**A**B Question How are the charges A and B related? A+, B-, A-, B+, A+, B-, A-, B+, A+, B-,