1. Welcome to Physics 7C! Lecture 5 -- Winter Quarter -- 2005 Professor Robin Erbacher 343 Phy/Geo erbacher@physics.ucdavis.edu

2. Announcements Course policy and regrade forms on the web: http://physics7.ucdavis.edu All lectures are posted on the web. Quiz today! ~20 minutes long on Block 12. Block 13 begins: DLMs 9, 10, and 11 this week. Turn off cell phones and pagers during lecture. If I’m speaking too loudly or softly, tell me!

3. Force Models In Physics 7B you learned about contact forces: normal and friction, gravitational, electric. We will call this the Direct Model of Forces It’s straightforward to think about a ball bouncing off the ground due to direct contact with the ground. But: How does Earth exert its gravitational force on the ball while in mid-air? This is an example of action-at-a-distance, and leads to Field Model of Forces Object A Object B exerts force field Object B exerts force Object A field creates

4. Recall: What is a Field? What is a Field? => a “map” of a measurable quantity Side out in MAP? = > spatial variation (x,y,z) * Temperature Scalars:* Elevation * Atmospheric Pressure Quantities?Scalar = magnitude only * Wind Velocity Vectors: * Gravity Field g = GM/r 2 * Electric Field E = kQ/r 2 Vector = magnitude and direction ex: velocity v {3 components… (v x,v y,v z ) } Bold means vector or overstrike arrow: v

5. Gravity Field Maps What is a Field? => a “map” of a measurable quantity Notice that the magnitude of the vectors increase for larger mass M: strength of field is greater!

6. Vector Addition Side out in Recall your vector addition rules: Whether we are discussing force vectors or field vectors, the rules of vector addition are simple. Always add vectors head-to-toe. Then it doesn’t matter what order you add them in. The length of a vector is in general proportional to the magnitude. The magnitude of a vector is a scalar: a simple numerical quantity. You can break it down into x and y components to add the vectors. ˆ ˆ

7. Gravitational Fields and Forces For gravity, we can think about an Object with mass M exerting a force on another object with mass m. Alternatively, we can think about an Object with mass M creating a gravitational field. This field would then act on any other object nearby, such as one with mass m. What does g depend on? What units does it have? In which direction does it point?

8. Alternatively, we can think about a charge Q creating an electric field. This field would then act on any other charges nearby, such as one with charge q. Electric Fields and Forces For electricity, we can use the direct force model similarly to gravity. Consider a charge Q exerting a force on a new charge q: What does E depend on?What units? In which direction does it point?

9. For an electric field E : Magnitude: Direction: out from +Q in toward -Q Electric Field/Force Directions For the coulomb force on a test charge q in a field E : Magnitude: Direction: along the E field vector for +q opposite the E field vector for -q q Q r

10. Electric Field Lines This is an Electric Dipole! Like charges (++) Opposite charges (+ -)

11. Electric Field Strengths Typical electric field strengths: 1 cm away from 1 nC of negative charge E = kq /r 2 = 10 10 * 10 -9 / 10 -4 =10 5 N /C Note: (N*m 2 /C 2 ) C / m 2 = N/C Fair weather atmospheric electricity = 100 N/C downward at 100 km high in the ionosphere Field due to a proton at the location of the electron in the H atom. (The radius of the electron orbit is 0.5*10 -10 m) E = kq /r 2 = 10 10 * 1.6*10 -19 / (0.5 *10 -10 ) 2 = 4*10 11 N /C q r E - - - - - - - - - E +++++ + Hydrogen atom 1 N / C = Volt / meter

12. Example: Calculating E Fields Finding an electric field from two charges: We have q 1 = +10 nC at the origin, q 2 = +15 nC at x=4 m. What is E at y=3 m and x=0? (point P) x y q 1 =10 nC q 2 =15 nC 4 3 P Use principle of superposition. ( Find x and y components of electric field due to both charges and add them up.)

13. Example: Calculating E Fields Recall: E =kq/r 2 x q 1 =10 nC q 2 =15 nC 4 5  y 3 E  Field due to q 1 : E = 10 10 N.m 2 /C 2 10 X10 -9 C/(3m) 2 = 11 N/C in the y direction. E y = 11 N/C E x = 0 Field due to q 2 : 10 10 N.m 2 /C 2 15 x10 -9 C/(5m) 2 = 6 N/C at some angle  Resolve into x and y components. E y = E sin   C E x = E cos   C Now add all components: E y = 11 + 3.6 = 14.6 N/C E x = -4.8 N/C Magnitude :    atan E y /E x = atan (14.6/-4.8)= 72.8 deg

14. Charge Induction Inducing Charge on a Net Neutral Object: How can a neutral object create an Electric field? (Where would the charges come from to produce such a field?) Static Electricity: Charge can be transferred from one object to another by rubbing. Static is the imbalance of positive and negative charges.

15. Gradient Relations: Potential Recall: What is the potential energy of a mass m in a the Earth’s gravitational field, a height h above the surface of the Earth? PE = mgh ! Force on a mass m in gravity field g is F = mg. Magnitude of force is the spatial derivative, or gradient, of the potential energy of the mass: The direction of the force on the mass m is toward decreasing PE grav (hence the negative sign!)

16. Gradients for E Fields: Potential Force on a charge q in an Electric field E is F = qE. Magnitude of force is the spatial derivative, or gradient, of the potential energy of the mass: The direction of the force on the charge +/- q is toward decreasing PE grav (hence the negative sign again!)