The World According to Physics 121

Transcription

1 The World According to Physics Objects Forces Specified by geometry and mass Gravity: F = G m m r m Others: Tension, Normal, Friction Space and Time uclidean with Galilean Invariance ordinary 3D space;; slow velocities r m

2 The World According to Physics Things -- Bodies and Fields (,B) Specified by geometry and mass and charge Forces Gravity: F = - G m m r r r m lectromagnetic: Space and Time m F = + v x B uclidean with Lorentz Invariance ordinary space but can be really really fast... v

3 F = 4πε 0 r F F F F elec F grav = m m 4 πε 0 G Superposition!!! F!

4 Your Lecture Thoughts Nervous about forces from multiple charges Questions about continuous line of charge We will continue on FRIDAY lectric Field Lines xample Calculations:» Discrete: lectric Dipole» Continuous: Infinite Line of Charge No new SmartPhysics due on Friday

5 Last time CheckPoint Four charged particles are placed on a circular ring with radius 3 m as shown below. A particle with charge Q is placed in the center of the ring 3 y x What is vertical force on Q? A) F y > 0 B) F y = 0 C) F y < 0 Q 3 is will have greater effect than the three charges, because two of the bottom charges are at an angle to the middle charge. - Nathan

6 Reminder: Coulomb's Law F r MKS Units: r in meters in Coulombs F in Newtons F Þ F = 4πε 0 r 4πε 0 = 9 x 0 9 N-m /C We call this group of constants k as in: F = k /r Same spatial dependence as gravitational force, NO mention of mass Strength determined by the charge of the two objects.

7 Clicker Two eual mass balls are suspended from the ceiling with eual length nonconducting threads as shown. Ball has charge Q = +3 and Ball has charge Q = +. Which of the following pictures best represents the euilibrium position? Q Q +3 + g +3 Q Q + Q +3 Q + Q Q +3 + (a) (b) (c)

8 Clicker Which of the following pictures best represents the euilibrium position? Q +3 Q + Q +3 Q + Q θ θ Q +3 + (a) Remember Newton s Third Law! (b) (c) The electrical force Q exerts on Q must be eual and opposite to the electrical force that Q exerts on Q. The amount of charge each ball has determines the magnitude of the force, but each ball experiences the same force. Therefore, the symmetry demands (c)!!

9 Consider more than two charges now If were the only other charge, we would know the force on due to. If were the only other charge, we would know the force on due to. What is the force on when both and are present?? As in mechanics, we have the Law of Superposition: The TOTAL FORC on the object is just the VCTOR SUM of the individual forces. F = F + F - F F + F +

10 Clicker What happens to the Force on if its sign is changed? A) F increases B) F remains the same C) F decreases D) Need more information to determine 4 3

11 Clicker What happens to the Force on if its sign is changed? A) F increases B) F remains the same C) F decreases D) Need more information to determine 4 3

12 The direction of all forces changes by 80 o the magnitudes stay the same: F 4, F 4, F, F, F F F 3, 4 F 3, 4 3 F F, F 3, 3 F F, F 3, F 4, F 4, F! = F + F + F...!!!, 3, 4, +!!! = F F F... F!, 3, 4,

13 The lectric Field A simple but profound observation The net Coulomb force on a given charge is always proportional to the strength of that charge. - F F + F +! F!! F!!! F = F + F r r = " " + πε r r 4 0 This is one important definition!!! We can therefore define a uantity, the electric field, which is independent of the test charge and depends only on the position in space:

14 The lectric Field! With this concept, we can map the electric field anywhere in space, produced by any arbitrary Collection of charges or Charge distribution! F! = 4 πε r i rˆ i i! d = rˆ 4πε 0 r

15 xample What is the electric field at the origin? y The fields from the top right and bottom left cancel + a a + The total field is from the top left charge only a a a The components are: x = 4πε 0 a y = 4πε 0 a a + x If a charge Q were placed at the origin, the force on this charge would be: F F y x = = Q Q y x Q = 4πε 0 a Q = 4πε a 0 Note: if Q>0, F= if Q<0, F=

16 Clicker y Two charges, Q and Q, fixed along the x-axis as shown, produce an electric field at a point (x,y) = (0,d) which is directed along the negative y-axis. Which of the following statements is true? (a) (b) (c) Both charges Q and Q must be positive. Both charges Q and Q must be negative. The charges Q and Q must have opposite signs. d Q Q x Q (a) Q Q (b) Q Q (c) Q

17 CheckPoint = k Q Q r 4r A B C D And for the motion, recall F = = ma (F, and a are vectors)

18 Clicker followup Same setup: Q has charge +Q Q has charge +Q They are separated by d. Charge is a distance a away from Q a d Is there a place the value for a -- between Q and Q where the force on ANY charge (positive or negative) is zero? (a) (b) (c) NO Yes, but I can t find it with all this time pressure. Yes and my answer is from Q. I will volunteer to specify if you ask me

19 Clicker followup a d Is there a place the value for a -- between Q and Q where the force on ANY charge (positive or negative) is zero? The force on charge a distance a away from Q is F = Q Q 4πε 0 a ( d a) = 0? True if: ( ) (c) Yes and my answer is a = d from Q. a = ( d a) for some value of a (you can check if that s right)

20 Clicker What is the direction of the electric field at point P, the unoccupied corner of the suare? d + P A) B) C) = 0 D) Need to know d + ) d Need to know d & Calculate at point P.! = i k Q r ˆ i r i i x = 4πε o d π cos ( ) d 4 > 0 y = 4πε o d π sin ( ) d 4 > 0

21 CheckPoints x y A +Q Q B Two eual, but opposite charges are placed on the x axis. The positive charge is placed to the left of the origin and the negative charge is placed to the right, as shown in the figure above. A? 4 ) B? (For point A) The electric field due to left charge is up and to the right (repulsive because both points are positive). The electric field due to right charge is down and to the right because points have different signs. The two electric fields have a net electric field to the right. - Andrea

22 CheckPoint In which case is the magnitude of the electric field at A the largest? +Q A +Q A Q +Q Case Case SAM

23 Reality of lectric Field The electric field has been introduced as a mathematical convenience, just as the gravitational field in Phys. Spoiler Alert: There is MUCH MOR to the electric field than this! IMPORTANT: field propagates at speed of light. NO instantaneous action at a distance!! (we will explore this aspect when we get to electromagnetic waves) As a charge moves, resultant field at time t depends on where the charge was at time t-dt. We avoid these complications for now by restricting ourselves to situations in which the SOURC of the field is AT RST! (i.e. electrostatics)

24 Force Comparison lectrical vs Gravitational F F m m F elec = 4 πε 0 r F grav = G m m r For a proton, * =.6 X 0-9 C m =.67 X 0-7 kg r F elec F grav = F F elec grav m m 4 πε 0 G + = * Note: smallest charge seen in nature!

25 We will do the Dipole See you Friday We will do the line of charge No new SP on Friday Start your Webassign HW soon please