Welcome to Physics 7C!

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. exerts force exerts force Object A Object B creates field Object B Object A field 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

4. MAP?= >spatial variation (x,y,z) * Temperature Scalars:* Elevation * Atmospheric Pressure Quantities?Scalar = magnitude only * Wind Velocity Vectors:* Gravity Fieldg = GM/r2 * Electric FieldE = kQ/r2 Vector = magnitude and direction ex: velocity v {3 components… (vx,vy,vz) } Side out in Bold means vector or overstrike arrow: v Recall: What is a Field? What is a Field? => a “map” of a measurable quantity

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. ˆ ˆ Side out in Vector Addition • 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.

7. 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? Gravitational Fields and Forces For gravity, we can think about an Object with mass M exerting a force on another object with mass m. 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 r q Q 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 Electric Field/Force Directions

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

11. r q E +++++ E - - - - - - - - - + Hydrogen atom Electric Field Strengths • Typical electric field strengths: • 1 cm away from 1 nC of negative charge • E = kq/r2=1010 *10-9/ 10-4 =105 N /C • Note:(N*m2/C2) C / m2 = 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/r2=1010 *1.6*10-19/ (0.5 *10-10 )2 = 4*1011 N /C 1 N / C = Volt / meter

12. y P 3 x 4 q2 =15 nC q1=10 nC Example: Calculating E Fields Finding an electric field from two charges: We have q1= +10 nC at the origin, q2 = +15 nC at x=4 m. What is E at y=3 m and x=0? (point P) Use principle of superposition. (Find x and y components of electric field due to both charges and add them up.)

13. y E  5 3  x 4 q2 =15 nC q1=10 nC Now add all components: Ey= 11 + 3.6 = 14.6 N/C Ex= -4.8 N/C Magnitude: Example: Calculating E Fields Recall:E =kq/r2 Field due to q1: E = 1010 N.m2/C2 10 X10-9 C/(3m)2 = 11 N/C in the y direction. Ey= 11 N/C Ex= 0 Field due to q2: 1010 N.m2/C2 15 x10-9 C/(5m)2 = 6 N/C at some angle Resolve into x and y components. Ey= E sin  = 6 * 3/5 =18/5 = 3.6 N/C Ex= E cos  = 6 * (-4)/5 =-24/5 = -4.8 N/C 1 = atan Ey/Ex= 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 PEgrav (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 PEgrav (hence the negative sign again!)