PHYSICS 272 Electric & Magnetic Interactions

Transcription

1 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions PHYSICS 272 Electric & Magnetic Interactions Lecture 5 Charging/Discharging; Efield of distributed charges: charged rod and ring [EMI 15.7; ] Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 1

2 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions A few reminders If you have problems/issues with your iclicker, please see VK Saxena (Office: PHYS 176; Phone: 49575; saxena@purdue.edu) iclicker code is CD for each lecture, keep power ON Saxena is also the person you should see if you have questions on WebAssign or CHIP. HW help/questions: Help Center, TA, Saxena, Prof. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 2

3 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Last time Insulators and Conductors What is Efield inside How do they interact with Efield What happen to charges/dipoles polarization Charging and Discharging Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 5 Slide 3

4 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Equilibrium condition inside a conductor: v 0 ( E 0) The drift is often stopped by collisions. Note: Later in the course, we will discuss DC current flowing in conductors that s a static but nonequilibrium situation [there can be E inside] Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 4

5 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Introduce this concept to metal: Drude Model E p Fnet (e) Enet t No net interaction between mobile electrons Forget previous velocity after collision p p 0 ee v v p m e et E m e e net eenett m net t et m (mobility) e Later we will show that conductivity () µ Some important sources of collision: impurities thermal motion of atoms (more motion at higher temperature T shorter t lower [common feature of metals]) Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 5

6 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Effect of excess charges on insulators or conductors on another conductor induction (a) insulator Conducting rod E dipoles Excess charge E excess (b) conductor Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 6

7 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Charging and Discharging Discharging by contact: On approach: body polarizes On contact: charge redistributes over larger surface Grounding: connection to earth (ground) very large object Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 5 Slide 7

8 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions How did we Neutralize a Tape? Negative charges attract positive charges Tape now acts as a series of dipoles much weaker than single charges, i.e., less force exerted external objects. Humidity (water molecules) often facilitates discharging Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 8

9 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 5 Slide 9

10 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions iclicker Remind: set code to CD at beginning of each lecture by holding on/off for 2 sec, and enter CD If you power off the iclicker you need to reset the code Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 10

11 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Clicker Question 1 Which of the following statements is true? A) A charged object is always repelled by a neutral object? B) A charged object is always attracted to a neutral object? C) A charged object is sometimes attracted and sometimes repelled by a neutral object? D) A charged object is not affected by a neutral object? Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 11

12 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Clicker Question 1 Which of the following statements is true? A) A charged object is always repelled by a neutral object? B) A charged object is always attracted to a neutral object? C) A charged object is sometimes attracted and sometimes repelled by a neutral object? D) A charged object is not affected by a neutral object? B Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 12

13 Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 5 Slide 13 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Question 2 A) B) C) D) E An electric field polarizes a metal block as shown below. Select the diagram that represents the final state of the metal.

14 Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 5 Slide 14 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Question 2 A) B) C) D) E An electric field polarizes a metal block as shown below. Select the diagram that represents the final state of the metal. B

15 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Chapter 16 Electric Field of Distributed Charges Key Ideas Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 5 Slide 15

16 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 5 Slide 16

17 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Uniformly Charged Thin Rod Length: L Charge: Q What is the pattern of electric field around the rod? Cylindrical symmetry Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 17

18 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions z is out of board rod and observation pt lie in (x,y) plane First: Set up coordinate system; Divide Distribution into Pieces observation pt. Apply superposition principle: Divide rod into small sections y with charge Q Assumptions: Rod is so thin that we can ignore its thickness. If y is very small Q can be considered as a point charge Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 18

19 E PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Q 2 r rˆ Step 2: E due to one Piece r obs.loc source x, y 0,0 0, y,0 r x, y 0 y,0 r x 2 y 0 y 2 ˆr x, y y 0,0 x 2 y 0 y 2 Q y L Q y integration variable r E Q x, y 0 y,0 2 L x 2 y 0 y Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide y

20 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Step 2: E due to one Piece r E Q x, y 0 y,0 2 L x 2 y 0 y 3 2 y E x 1 Q 4 0 L E y 1 Q 4 0 L Components of E: x x 2 y 0 y 2 y 0 y x 2 y 0 y y y E z 0 Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 20

21 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Step 3: Add up Contribution of all Pieces Simplified problem: find electric field at the location <x,0,0> E y E1, y E2, y E3, y... Ei, i y E y 0 E x E i, Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 21 i E i,x 1 Q 4 0 L E x i x 1 Q 4 0 L x x 2 y 0 y 2 i i x 3 x 2 2 y i 2 E x Q L x 1 3 x 2 2 y i 2 y y 3 2 y

22 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions i E x Q L x 1 3 x 2 2 y i 2 y Integration: taking an infinite number of slices E x lim y0 1 Q 4 0 L x 1 i E x Q L x 1 Step 3: Add up Contribution of all Pieces L 2 L 2 1 dx (a 2 x 2 ) 3/2 3 x 2 2 y i 2 3 x 2 y 2 2 x dy Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 22 y a 2 a 2 x 2 definite integral

23 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Step 3: Add up Contribution of all Pieces L 2 E x Q L x 1 L 2 3 x 2 y 2 2 dy Evaluating integral: E x E x Q L x y x 2 x 2 y 2 Q x x 2 L / 2 2 L 2 L 2 Cylindrical symmetry: replace xr E y Q r r 2 L / 2 2 Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 23

24 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions E of Uniformly Charged Thin Rod At center plane In vector form: Check the results: Direction: E y Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 24 Q r r 2 L / 2 2 ˆr Units: Special case r>>l: E y0 1 Q 4 0 r 2 ˆr Compare with numerical calculation: L=1 m, r=0.5 m E y0 Q Q 4 0

25 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions Special Case: A Very Long Rod E y Very long rod: L>>r E y E y Q r r 2 L / 2 2 1/r dependence! Q r L / Q / L r ˆr ˆr ˆr Q/L linear charge density Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 25

26 PHYS 272: Matter and Interactions II Electric And Magnetic Interactions General Procedure for Calculating Electric Field of Distributed Charges 1. Cut the charge distribution into pieces for which the field is known 2. Write an expression for the electric field due to one piece (i) Choose origin (ii) Write an expression for E and its components 3. Add up the contributions of all the pieces (i) Try to integrate symbolically (ii) If impossible integrate numerically 4. Check the results: (i) Direction (ii) Units (iii) Special cases Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 5 Slide 26