1 Physics 8.02T For now, please sit anywhere, 9 to a table

2 Course Details We will not go over the course details in class, you can find them at Or go directly to Are their any burning questions about course details?

3 W01D2: Outline Introductions Course Overview Vector and Scalar Fields Charge Electric Force Electric Field

Introductions

Announcements Math Review Tuesday Tues Feb 14 from 9-11 pm in PS 1 due Tuesday Tues Feb 14 at 9 pm in boxes outside or W01D3 Reading Assignment Course Notes: Chapter , Bring Clickers to Monday/Tuesday Class 5

6 8.02: Electricity and Magnetism Also new way of thinking… How do objects interact at a distance? Fields We will learn about electric & magnetic fields: how they are created & what they affect Maxwell’s Equations Lorentz Force Law

7 Scalar and Vector Fields Review Vector Analysis in Online Course Notes

8 Scalar Fields Temperature Scalar Field: every location has an associated value (number with units)

9 Scalar Fields - Contours Colors represent surface temperature Contour lines show constant temperatures

10 Vector Fields Vector (magnitude, direction) at every point in space Example: Velocity vector field - jet stream

11 Coulomb’s Law, Electric Fields and Discrete Charge Distributions

12 Electric Charge Two types of electric charge: positive and negative Unit of charge is the coulomb [C] Charge of electron (negative) or proton (positive) is Charge is quantized Charge is conserved

13 Electric Force The electric force between charges q 1 and q 2 is (a) repulsive if charges have same signs (b) attractive if charges have opposite signs Like charges repel and opposites attract !!

14 Coulomb's Law Coulomb’s Law: Force on q 2 due to interaction between q 1 and q 2 unit vector from q 1 to q 2 vector from q 1 to q 2

15 Coulomb's Law: Example a = 1 m q 1 = 6 C q 3 = 3 C q 2 = 3 C

16 The Superposition Principle Many Charges Present: Net force on any charge is vector sum of forces from other individual charges Example: In general:

17 In Class Problem: Force on a Charged Object Three charged objects are located at the positions shown in the figure. Find a vector expression for the force on the negatively charged object located at the point P. NOTE: Solutions will be posted within two days of class

18 Charging

19 How Do You Get Charged? Friction Transfer (touching) Induction +q Neutral

20 Demonstrations: Instruments for Charging

21 Electric Field

22 Electric Field The electric field at a point P due to a charged object (source) with charge q s is the force acting on a test point-like charged object with charge q t at that point P, divided by the charge q t : Units: N/C

23 Superposition Principle The electric field due to a collection of N point charges is the vector sum of the individual electric fields due to each charge

24 Concept Question: 5 Equal Charges Six equal positive charges q sit at the vertices of a regular hexagon with sides of length R. We remove the bottom charge. The electric field at the center of the hexagon (point P) is:

25 Concept Question Answer: 5 Equal Charges E fields of the side pairs cancel (symmetry) E at center due only to top charge (R away) Field points downward Alternatively: “Added negative charge” at bottom R away, pulls field down Answer 4.

26 Group Problem: Electric Field on Axis (Symmetry) Consider two point charges of equal magnitude but opposite signs, separated by a distance d. Point P lies along the perpendicular bisector of the line joining the charges, a distance s above that line. What is the E field at P?

27 Electric Field Lines 1.Direction of field at any point is tangent to field line at that point 2.Field lines point away from positive charges and terminate on negative charges 3.Field lines never cross each other

28 Concept Question: Field Lines Electric field lines show: 1.Directions of forces that exist in space at all times. 2.Directions in which positive charges on those lines will accelerate. 3.Paths that charges will follow. 4.More than one of the above.. 5.I don’t know.

29 Concept Question Answer: Field Lines NOTE: This is different than flow lines (3). Particles do NOT move along field lines. (1) is not correct because we don’t know sign of charge so we don’t know direction of force Answer: 2. Directions positive charges accelerate.

30 Force on a Charge Object in an Electric Field Force on a charged object with charge q at a point P in an electric field due to a source is:

31 Summary Charge q s (±) CREATE: FEEL: SOURCE:

32 Concept Question: Electric Field Two charged objects are placed on a line as shown below. The magnitude of the negative charge on the right is greater than the magnitude of the positive charge on the left,. Other than at infinity, where is the electric field zero? 1.Between the two charged objects. 2.To the right of the charged object on the right. 3.To the left of the charged object on the left. 4.The electric field is nowhere zero. 5.Not enough info – need to know which is positive.

33 Concept Question Answer: Electric Field Answer: 3. To the left of the positively charged object on the left Between: field points from positively charged object to negatively charged object On right: field is dominated by negatively charged object On left: electric field due to close smaller positively charged object will cancel electric field due to further larger negatively charged object.