1 From Last Time… Forces between charges Electric dipole

2 Exam 1 Wed. Feb. 20, 5:30-7 pm Covers Chap , 22-23, lecture, lab, discussion, HW Review Group/Quiz (solutions on website). Review lab question sheets. Review sample exams on website. HW4 (due Fri. next week) covers exam material. Students with schedule class conflicts: stay after lecture today to arrange time 8 1/2 x 11 handwritten note sheet (both sides) allowed

3 From Last Time… Forces between charges Electric dipole

4 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.

5 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.

6 Electric field of a point charge + + Force on this charge… …due to this charge Q1Q1 Q2Q2 = Force/unit charge Units? N/C

7 Question Which vector best represents the electric field at the red dot? - A B C - D E

8 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.

9 Relationship Between F and E F e = qE  This is valid for a test charge small enough that it does not disturb the source charge distribution If q is positive, F and E are in the same direction + r = 1x m Q p =1.6x C E (to the right) Electric field 1Å away from proton

10 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

11 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 q 1, E 1 Find the electric field due to q 2, E 2 E = E 1 + E 2 Remember, the fields add as vectors

12 Quick Quiz Which is the direction of the electric field at dot? A. Left B. Right C. Up D. Down E. Zero + - x y Away from positive charge (right) Net E field is to right.

13 Quick Quiz In this electric dipole, what is the direction of the electric field at point A? A)Up B)Down C) Left D) Right E) Zero +Q+Q-Q-Q x=+ a x=- a A

14 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.

15 Calculating dipole electric field On the y-axis + - x y For Since points from - charge to + charge on y-axis of dipole only

16 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 B A) B) C) D)

17 Pictorial representation of E: Electric Field Lines

18 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

19 Point particles

20 Electric field of a dipole + -

21 Electric field of two + charges

22 Question How are the charges A and B related? A)A+, B-, B)A-, B+, C)A+, B-, D)A-, B+, E)A+, B-, A B

23 Hydrogen Atom Example The magnitude of the electric force between the electron and proton:  F e = k e |e| |-e| / r 2 = 8.2 x N, r ~ 0.53 x m The gravitational force between the electron and the proton  F g = Gm e m p / r 2 = 3.6 x N m e = 9.11 x kg, m p = 1.67 x kg G = 6.67 x N m 2 /kg 2 F e /F g ~ 2 x r = 0.53x m M p =1.67x kg M e = 9.11 x kg