The Electric Field I

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					The Electric Field I

 Electric field for a point charge
Electric field for multiple charges
               Dipole
       Electric Field Lines
            Reading Questions
Who wants an A in General Physics II? What should I do
to get an A.
    1.   Work harder on the homework.
    2.   Make sure I read and study before class.
    3.   Do the questions in the Student Workbook.
    4.   Study at least 4 hours for the exams.
    5.   All of the above.
               Reading Questions
Who wants an A in General Physics II? What should I do
to get an A.
    1.   Work harder on the homework.
    2.   Make sure I read and study before class.
    3.   Do the questions in the Student Workbook.
    4.   Study at least 4 hours for the exams.
    5.   All of the above.
            Reading Questions
The electric field of a charge is defined by the force on
       1. an electron.
       2. a proton.
       3. a source charge.
       4. a test charge.
            Reading Questions
The electric field of a charge is defined by the force on
       1. an electron.
       2. a proton.
       3. a source charge.
       4. a test charge.
            Reading Questions
Charges A and B exert repulsive forces on each other.
qA = 4qB. Which statement is true?




                     1. FA on B > FB on A
                     2. FA on B < FB on A
                     3. FA on B = FB on A
            Reading Questions
Charges A and B exert repulsive forces on each other.
qA = 4qB. Which statement is true?




                     1. FA on B > FB on A
                     2. FA on B < FB on A
                     3. FA on B = FB on A
             Reading Questions
Charges A and B exert repulsive forces on each other.
qA = 4qB. Point P is midway between A and B. Which
statement is true?

1. EA > EB
2. EA < EB                               P
3. EA = EB
             Reading Questions
Charges A and B exert repulsive forces on each other.
qA = 4qB. Point P is midway between A and B. Which
statement is true?

1. EA > EB
2. EA < EB                               P
3. EA = EB
            Reading Questions
An electron is placed at the position marked by the dot.
The force on the electron is

   1. to the left.
   2. to the right.
   3. zero.
   4. There’s not enough
       information to tell.
            Reading Questions
An electron is placed at the position marked by the dot.
The force on the electron is

   1. to the left.
   2. to the right.
   3. zero.
   4. There’s not enough
       information to tell.
             Reading Questions
Rank in order, from largest to smallest, the electric field
strengths E1 to E4 at points 1 to 4.



                  1. E2 > E4 > E1 > E3
                  2. E2 > E1 = E4 > E3
                  3. E2 > E1 > E4 > E3
                  4. E1 = E2 > E3 = E4
                  5. E1 > E2 > E3 > E4
             Reading Questions
Rank in order, from largest to smallest, the electric field
strengths E1 to E4 at points 1 to 4.



                  1. E2 > E4 > E1 > E3
                  2. E2 > E1 = E4 > E3
                  3. E2 > E1 > E4 > E3
                  4. E1 = E2 > E3 = E4
                  5. E1 > E2 > E3 > E4
           Reading Questions
What device provides a practical way to produce
a uniform electric field?
      1. A long thin resistor
      2. A Faraday cage
      3. A parallel plate capacitor
      4. A toroidal inductor
      5. An electric field uniformizer
           Reading Questions
What device provides a practical way to produce
a uniform electric field?
      1. A long thin resistor
      2. A Faraday cage
      3. A parallel plate capacitor
      4. A toroidal inductor
      5. An electric field uniformizer
                   The Electric Field
  Electric Field
  •   Write the definition for the electric field.
                                            
         F                                 FQ ,q
        E              or            EQ 
           q                                     q
the charge q is called
a “test” charge
                                     FQ,q
                                 q          EQ

                                             We believe that if we take
                           r               away the charge q the
               Q
                                           electric field from Q
                                             remains
                   The Electric Field
    Electric Field for a Point Charge
     Write Coulomb’s law for a point charge.
                    Qq ˆ                                       FQ,q
          FQ,q    k 2 rQ,q
                    rQ,q                                   q          EQ
   Use Coulomb’s law and the
   definition for the electric field to
   find the relationship (equation) for Q   r

   the electric field for a point charge.    
                              Qq
                                     ˆ
                              k 2 rQ ,q
                FQ ,q        rQ ,q         Q             Q
      E  EQ                            r
                                          k 2 r  ˆQ ,q  k 2 r
                                                              ˆ
                    q            q           Q ,q          r
            The Electric Field
Electric Field for a Negative Point Charge
             The Electric Field
Superposition
Recall that if we have       
more than one charge the     E
total force is just the
vector sum.
     
   F  F1  F2
The same is true for the
electric field.
    
  E  E1  E2
The Electric Field
            Reading Questions
A proton is placed at the position marked by the dot.
The force on the proton is

   1. to the left.
   2. to the right.
   3. zero.
   4. There’s not enough
       information to tell.
            Reading Questions
An electron is placed at the position marked by the dot.
The force on the electron is

   1. to the left.
   2. to the right.
   3. zero.
   4. There’s not enough
       information to tell.
             Reading Questions
Rank in order, from largest to smallest, the electric field
strengths E1 to E4 at points 1 to 4.



                  1. E2 > E4 > E1 > E3
                  2. E2 > E1 = E4 > E3
                  3. E2 > E1 > E4 > E3
                  4. E1 = E2 > E3 = E4
                  5. E1 > E2 > E3 > E4
             Reading Questions
Rank in order, from largest to smallest, the electric field
strengths E1 to E4 at points 1 to 4.



                  1. E2 > E4 > E1 > E3
                  2. E2 > E1 = E4 > E3
                  3. E2 > E1 > E4 > E3
                  4. E1 = E2 > E3 = E4
                  5. E1 > E2 > E3 > E4
Student Workbook
Student Workbook
Student Workbook
Student Workbook

ˆ
r
Student Workbook
Student Workbook
   Student Workbook
For a true point charge the field can go in two
directions at the charge but must have the same
magnitude and would be infinite.




    Knight goofed! These are not electric field lines
    but electric field vectors. You could have a
    negative charge here.
Student Workbook
Student Workbook
Student Workbook




   Symmetry
Student Workbook
Student Workbook
            Student Workbook




If the string of charges is not infinite, then the outside
electric fields should be smaller in magnitude
Student Workbook
                Class Questions
At the position of the dot P,
the electric field points
    1. Left.
    2. Down.
    3. Right.
    4. Up.                           P
    5. The electric field is zero.
                Class Questions
At the position of the dot P,
the electric field points
    1. Left.
    2. Down.
    3. Right.
    4. Up.                           P
    5. The electric field is zero.
                 The Electric Field
•   A point charge of -15 mC is placed at the origin as shown.


                        .2
                                         E
                   15mC
                                    .2       .4

                        
          


•   What is the electric field at x = 0.4 m, y = 0.2 m. Don’t
    forget that the electric field is a vector so give me the
    magnitude and direction.
                         The Electric Field
         What is the electric field at x = 0.4 m, y = 0.2 m. Don’t forget
         that the electric field is a vector so give me the magnitude and
         direction.
         First we must find the magnitude of r.

             r  r  x 2  y 2  (0.4m) 2  (0.2m) 2  0.45m
         Next the direction of r.
                1 y       1 0.2m
           tan ( )  tan (       )  tan1(0.5)  26.60 ,206.60
                   x          0.4m
    
         The magnitude for the electric field.
                Q
                  ˆ  (9X10 9 Nm 2 )
         E E k 2r
                                2           15X106 C 
                                                             6.8X10 5 N
                                 C                                        C
                r                              (0.45m) 2
                    The Electric Field
   •   Rewrite the electric field at x =0.4 m, y = 0.2 m using unit
       vectors i and j.
                       Q
          E  E  k 2 r  6.8X10 5 N
                         ˆ
                       r                C
                  1 y
           tan ( )  26.60,206.60
                     x
 E  E cos  6.8X10 5 N C cos206.6 0  6.1X10 5 N C
    x

 E  E sin   6.8X10 5 N C sin 206.6 0  3.0X10 5 N C
    y


   •   Draw an arrow to represent the electric field. Place the
       arrow so that the end is at x = 0.4 m, y = 0.2 m and let 1 cm
       represents a magnitude of 2.0 X105 N/C.
              The Electric Field
                                        Ex

E  E  6.8X10 5 N          1 cm
                      C                      Ey
                      .2           r
  26.6 ,206.6
        0         0




                               .2       .4


E x  6.1X10 5 N C
E y  3.0X10 5 N C
                  The Electric Field
•   Consider the two charges -15 mC and 6 mC shown below.
    Use the superposition principle to find the electric field at
    x = 0.4, y = 0.2 m due to both charges.

                y (m)




                   .2



             15mC                                  6mC


                                  .2           .4         x (m)
                                        
    
                      The Electric Field
     •   The electric field due to the -15 mC charge is the same as
         before.
           E x  6.1X10 5 N C
           E y  3.0X10 5 N C

     •   Next find the electric field (in terms of unit vector) for the
         6 mC charge.
         Ex  0
                  Q                       6X106 C
           E y  k 2  (9X10 9 Nm 2 C 2 )           13.5X10 5 N C
                  r                       (0.2m) 2

     Now what do we need to do?
                      The Electric Field
     Add the two fields vectorally.

      E x  6.1X10 5 N C
      E y  3.0X10 5 N C  13.5X10 5 N C  10.5X10 5 N C
                                           E           E6
              y (m)
                 .2


                                           E-15



                                      .2          .4    x (m)
              The Electric Field
•   Electric Dipole

                                   E ~ 1/r3



p  qdrp
      ˆ       dipole moment
                       The Electric Field
•    Force and Torque on an Electric Dipole in Electric Field
                                                    
        F  F  F  0           r F       or        pE
                                 
                                  r  F  2rF sin 
                                 
                                  2 rqE sin   pE sin 
                                               
                                              pE
                                U  p  E  pE cos

    Dipole in a non-
    uniform field
                 
    F  F  F  0
              The Electric Field
•   Microwave Oven
                       For an electromagnetic wave the
                       electric field is much larger than
                       the magnetic field.




                       picture of microwave oven
                The Electric Field
• Matter in an Electric Field
    
  F                        
 E                    F  qE
    q
Student Workbook
Student Workbook
Student Workbook
Student Workbook
               Class Questions
Rank in order, from largest to
smallest, the forces Fa to Fe a proton
would experience if placed at points a
– e in this parallel-plate capacitor.
    1.   Fa = Fb = Fc = Fd = Fe
    2.   Fa = Fb > Fc > Fd = Fe
    3.   Fa = Fb = Fd = Fe > Fc
    4.   Fe > Fd > Fc > Fb > Fa
    5.   Fe = Fd > Fc > Fa = Fb
               Class Questions
Rank in order, from largest to
smallest, the forces Fa to Fe a proton
would experience if placed at points a
– e in this parallel-plate capacitor.
    1.   Fa = Fb = Fc = Fd = Fe
    2.   Fa = Fb > Fc > Fd = Fe
    3.   Fa = Fb = Fd = Fe > Fc
    4.   Fe > Fd > Fc > Fb > Fa
    5.   Fe = Fd > Fc > Fa = Fb
                Class Questions
  Which electric field is responsible for
  the trajectory of the proton?




(1)       (2)       (3)       (4)     (5)
                 Class Questions
  Which electric field is responsible for
  the trajectory of the proton?




(1)        (2)      (3)       (4)     (5)


How would the motion change if it was an electron?