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					           Physics 212
              Lecture 5
          Today's Concept:
    Electric Potential Energy
Defined as Minus Work Done by Electric Field




                                 Physics 212 Lecture 5, Slide 1
                                 Music
Who is the Artist?

A)   Tito Puente
B)   Buena Vista Social Club
C)   Louis Prima
D)   Freddie Omar con su banda
E)   Los Hombres Calientes
                                    Cuban Jazz !!

                     Thanks to Ry Cooder for bringing these guys
                                  to our attention !!
                                        Why ??

                            Cuban Jazz at Krannert (Ellnora)
                                Friday night (10:30pm)
                             Marc Ribot y Cubanos Postizos
                            Remembering Arsenio Rodriguez

                                         FREE
                                                               Physics 212 Lecture 5
                                Your Comments
     “This really seems like a rehash of mechanics with electric          Right! Nothing
     charges instead of masses.”                                            really new

     “Please discuss in lecture about how the point charges will affect the
     electric field in different situations where it has both same charge or
     where it has opposite charges. I am confused about this. Also,               SIGNS!
     please go over the potential energy equation to refresh my memory.”
     “When solving for the potential energy, does r1 get subtracted from
     r2? or is it the other way around?”
     “Homework problem style examples would be helpful, the
     checkpoints felt too easy.”                                       Example today:
     “Still generally confused on some questions about the           calculation for CP 3
     potential energy, like the third checkpoint.”
                                                                     Discussion Sections
     “Had there been office hours this week I definitely would have this week should help
     been there. I'm still not 100% sure about Gauss' Law.”               WORKED
                                                                         EXAMPLES!

     “Labor Day Weekend and Physics must definitely have the same charge because the
     weekend kept pushing the homework and this prelecture from getting done.”
05
                                                                    Physics 212 Lecture 5, Slide 3
                                   r2
    Recall from physics 211:
                               W   F dr          WTOT   K
                                   r1

                    F                   Object speeds up ( K > 0 )
                    dr     W>0


                    F
                    dr
           or
                           W<0          Object slows down ( K < 0 )
                    F
                    dr


                F
                          W=0           Constant speed ( K = 0 )
                     dr
9
                                                 Physics 212 Lecture 5, Slide 4
                Potential Energy



  U  Wconservative
If gravity does negative work, potential energy increases!
Same idea for Coulomb force… if Coulomb force does
negative work, potential energy increases.

                                    F
          +                   +


                         x       Coulomb force does negative work
          +         +                Potential energy increases

                                             Physics 212 Lecture 5, Slide 5
                                Checkpoint 4
A charge is released from rest in a region of electric field. The charge will start to move

A) in a direction that makes its potential energy increase
B) in a direction that makes its potential energy decrease
C) along a path of constant potential energy

                                            “Since potential energy is negative, the charge will
                                            try to increase its potential energy, bringing it to
                                            zero..”

                                            “It wants to go to a spot with less PE.”

                                            “constant potential energy would require no work to
                                            preform.”


                                              It will move in the same direction as F
                                   F
                                               Work done by force is positive
                 x
                                               U = -Work is negative
     Nature wants things to move in such a way that PE decreases
34
                                                                    Physics 212 Lecture 5, Slide 6
            Example: Charge in External Field
     You hold a positively charged ball and walk due west in a
     region that contains an electric field directed due east.

                          FE             FH
                                              dr
                     E

            WH is the work done by the hand on the ball
            WE is the work done by the electric field on the ball

            Which of the following statements is true:

            A)   WH > 0   and WE > 0
            B)   WH > 0   and WE < 0
            C)   WH < 0   and WE < 0
            D)   WH < 0   and WE > 0
14
                                                   Physics 212 Lecture 5, Slide 7
                                       Not a conservative force.
 Conservative force: U = - WE          Does not have any U.


                        FE            FH
                                           dr
                   E

                   B) WH > 0 and WE < 0


                 Is U positive or negative?

                 A) Positive
                 B) Negative



16
                                                Physics 212 Lecture 5, Slide 8
            Example: Getting the signs right

                   Case A
                                  d
                   Case B
                                      2d



     In case A two negative charges which are equal in magnitude are
     separated by a distance d. In case B the same charges are separated
     by a distance 2d. Which configuration has the highest potential
     energy?

     A) Case A
     B) Case B




22
                                                    Physics 212 Lecture 5, Slide 9
                  Example: Getting the signs right
                                                           q1q2 1
• As usual, choose U = 0 to be at infinity:       U (r ) 
                                                           4 0 r
                                     q2 1
     Case A                    UA 
                      d             4 0 d
     Case B                                         q2 1
                                              UB 
                          2d                       4 0 2d

         U(r)




                                                                     UA > UB
          U(d)
         U(2d)
              0                                                                    r



23
                                                          Physics 212 Lecture 5, Slide 10
                    Example: Two Point Charges

     Calculate the change in potential energy for two point charges
     originally very far apart moved to a separation of “d”

                d
                  q1q2
        U    k 2 dr                       d
               
                   r12              q1                  q2


                                      q1q2           1 q1q2
                               U  k             
                                       d            4 0 d

      Charged particles w/ same sign have an increase in potential
      energy when brought closer together.


     For point charges often choose r=infinity as “zero” potential energy.


19
                                                       Physics 212 Lecture 5, Slide 11
                                          Checkpoint 1
A charge of +Q is fixed in space. A second charge of +q was first placed at a distance r1
away from +Q. Then it is moved to a new position at a distance R away from its starting
point on a straight path. The final location of +q is at a distance r2 from +Q.




What is the change in the potential energy of the
charge +q in the process?                                                  1 Qq                    1 Qq
A. kQq/R            B. kQqR/r12          C. kQqR/r22        U initial                U final 
D. kQq(1/r2 - 1/r1) E. kQq(1/r1 - 1/r2)                                   4 0 r1                4 0 r2

     “It is inversely proportional to the first radius.”
                                                                                        Qq  1 1 
     “Simple conservation of energy problem: final                 U  U f  U i             
     potential minus initial potential should equal                                    4 0  r2 r1 
     change. ”
                                                           Note: +q moves AWAY from +Q.
     “1/r1 will be larger then 1/r2 and this must be       Its Potential energy MUST DECREASE
     positive”                                                              U < 0

34
                                                                             Physics 212 Lecture 5, Slide 12
            Potential Energy of Many Charges

     Two charges are separated by a distance d. What is the change in
     potential energy when a third charge q is brought from far away to a
     distance d from the original two charges?

                                                         Q2


                                                   d                d
              qQ1 1 qQ2 1
         U         
              4 0 d 4 0 d
              (superposition)                 Q1                         q

                                                          d




25
                                                       Physics 212 Lecture 5, Slide 13
               Potential Energy of Many Charges
       What is the total energy required to bring in three identical
       charges, from infinitely far away to the points on an equilateral
       triangle shown.

       A) 0                                        Q
                      2
                  Q   1
       B) U  4
                   0 d
                                                                             3 Q2
                  Q2 1
       C) U  2 4 d                      d          d       W   Wi  
                     0
                                                                            40 d
                    2
       D) U  3 Q 1
                 4 0 d                                                 3 Q2
                  Q2 1                                           U  
       E) U  6                                                        40 d
                 4 0 d              Q            d       Q

     Work to bring in first charge:       W1 = 0
                                              1 Q2
     Work to bring in second charge : W2  
                                             40 d
                                              1 Q2   1 Q2      2 Q2
      Work to bring in third charge : W3                
                                             40 d 40 d    40 d

27
                                                                 Physics 212 Lecture 5, Slide 14
               Potential Energy of Many Charges

       Suppose one of the charges is negative. Now what is the total
       energy required to bring the three charges in infinitely far away?
                                                       2
       A) 0                                        Q

                   Q2 1
       B) U  1 4 d                                                          1 Q2
                       0
                                            d              d       W   Wi  
                                                                                40 d
                      2
                   Q 1
       C) U  1 4 d
                        0
                     2
       D)U  2 Q 1                                                 U  
                                                                             1 Q2
                  4 0 d
                    Q2 1                                                    40 d
       E) U  2                 1
                                      Q            d           Q
                   4 0 d

     Work to bring in first charge:       W1 = 0
                                              1 Q2
     Work to bring in second charge : W2  
                                             40 d
                                                  1 Q2   1 Q2
      Work to bring in third charge :     W3                0
                                                 40 d 40 d
29
                                                                    Physics 212 Lecture 5, Slide 15
                                      Checkpoint 2
Two charges which are equal in magnitude, but opposite in sign, are place at equal distances
from point A.




If a third charge is added to the system and placed at point A, how does the electric potential
energy of the charge collection change?
A. Increases          B. decreases        C. doesn’t change
D. The answer depends on the sign of the third charge


     “inserting another charge is going to increase the magnitude of the potential energy.”
     “No matter what the sign is the potential energy would be a positive number minus a negative
     number minus another negative number. ”
     “the change in potential is found by adding another kqq/r term. this term is dependent on the
     sign of the new charge.“
31
                                                                        Physics 212 Lecture 5, Slide 16
                                    Checkpoint 3
You start with two point charges separated by some distance. The charge of the first is
positive. The charge of the second is negative and its magnitude is twice as large as that of
the first.




Is it possible to find a place to which you can bring a third charge in from infinity without changing
the total potential energy of the system?
A. YES, as long as the third charge is positive       B. YES as long as the third charge is negative
C. YES, no matter what the third charge is            D. NO

                                                   “The positive third charge will cancel out the
                                                   negative charge.“

                                                   “It doesn't matter what the sign is. Place the new
                                                   charge twice the distance from the - as the +
                                                   charge. It doesn't matter what the sign is because
                                                   the U added to the system will now be zero.”

                                                   “Adding a third charge that is opposite to at least
                                                   one other charge will cause a change in potential
                                                   energy”

                                                     LET’S DO THE CALCULATION !!
34
                                                                         Physics 212 Lecture 5, Slide 17
              Example: Potential Energy Changes

     A positive charge q is placed at x=0 and a negative charge -2q is placed
     at x=d. At how many different places along the x axis could another
     positive charge be placed without changing the total potential energy of
     the system?


                       q                   -2q
                                                                                x
                      X=0                  X=d

         A)   0
         B)   1
         C)   2
         D)   3




37
                                                       Physics 212 Lecture 5, Slide 18
               Example: Potential Energy Changes

     At which two places can a positive charge be placed without changing the
     total potential energy of the system?




                       q                   -2q
      A               X=0     B     C                                D
                                                                               x
                                          X=d

          A)   A&B
          B)   A&C
          C)   B&C          Let’s calculate the positions of A and B
          D)   B&D
          E)   A&D




40
                                                      Physics 212 Lecture 5, Slide 19
              Lets work out where A is
         r                  d

                 q                -2q
     A          X=0
                                                                          x
                                  X=d


                     1 Qq   1 2Qq
             U         
                    40 r 40 r  d

                Set U = 0


                     1   2
                       
                     r rd


                                              Makes Sense!
                      rd       Q is twice as far from -2q as it is from +q

43
                                                 Physics 212 Lecture 5, Slide 20
              Lets work out where B is
                      r          d-r

                 q                         -2q
                                                                                    x
                X=0       B                X=d



                                       1   2
     Setting U = 0                      
                                       r d r



                                       2r  d  r


                                              d
                                         r
                                              3
                           Makes Sense!
             Q is twice as far from -2q as it is from +q   Physics 212 Lecture 5, Slide 21
46
                                   Summary

              For a pair of charges:                           r
                                q1q2
           Just evaluate   U k                    q1                       q2
                                  r
         (We usually choose U = 0 to be where the charges are far apart)



   For a collection of charges:
                q1q2
Sum up     U k             for all pairs
                  r




                                                             Physics 212 Lecture 5, Slide 22

				
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