PowerPoint Presentation

							Voltage and Capacitance

       Chapter 29
        Electric Potential Energy
Potential Energy of a charge
• Wants to move when it has
  high PE
• Point b
  – U = max
  – K = min
• Point a
  – U = min
  – K = max
               Electric Work
Charge moving between plates.

Work = FDr cos0o = qExf - qExi
DU = qExf - qExi
A 2.0 cm X 2.0 cm capacitor has a 2.0 mm spacing
  and a charge of +1.0 nC.
a. Calculate the electric field of the capacitor. (2.82 X
   105 N/C)
b. A proton is released from rest at the positive plate.
   Calculate the change in potential energy. (9.02 X
   10-17 J)
c. Calculate the final speed of the proton. (3.29 X 105
   m/s)
d. An electron is released from the halfway point
   between the plates. Calculate the change in PE and
   the final speed of the electron. (9.95 X 106 m/s)
A 2.0 cm diameter disk capacitor has a 2.5 mm
  spacing and a charge of +0.75 nC.
a. Calculate the electric field of the capacitor.
b. An electron is released from rest at the negative
   plate. Calculate the change in potential energy.
   (9.02 X 10-17 J)
c. Calculate the final speed of the electron. (3.29
   X 105 m/s)
  Potential Energy of point charges
Uelec = 1 q1q2
       4peo r

k = 9.0 X 109 Nm2/C2
A proton is fired from “far away” at a 1.0 cm
  diameter glass sphere of charge +100 nC.
a. Calculate the initial potential energy of the
   system (just as it touches the sphere).
b. Since PE = KE, calculate the needed initial
   speed of the proton.
An electron and a positron are created in the CERN
  collider.
a. Calculate the potential energy they have when
   they are 1.0 X 10-10 m apart.
b. Calculate the velocity they need to escape from
   one another. Remember that PE = KE, but you
   will need to consider the KE of both particles
   added together.
       Electric Potential: Voltage
• Voltage
• 1 Volt = 1 Joule/Coulomb

V = DU
    q

Vab = Va – Vb = -Wba         Work done by the
                             electric field to
                  q          accelerate the
                             charge
• The higher the rock, the greater the PE
• The greater the Voltage or charge, the greater the
  PE (DU = qV)
An electron is accelerated in a TV tube through a
  potential difference of 5000 V.
a. Calculate the change in PE of the electron (-8.0
    X 10-16 J)
b. Calculate the final speed of the electron (m = 9.1
    X 10-31 kg) (4.2 X 107 m/s (1/7th speed of light)
Calculate the final speed of a proton (mass =
 1.67 X 10-27 kg) (9.8 X 105 m/s (0.3% speed of
  light)
           Equipotential Lines
• Equipotential lines are
  perpendicular to electric field
  lines
• Voltage is the same along
  equipotential lines
• Like contour (elevation) lines on
  a map
Equipotential lines for point charges
        Electric Field and Voltage
U = qEs
V = DU/q
V = Es

Greater the distance between plates, the greater the
 voltage
The greater the E field, the greater the voltage
Voltage increases as you move between plates
What is the electric field between two plates
 separated by 5.0 cm with a voltage of 50V. (1000
 V/m)
A capacitor is constructed of 2.0 cm diameter
  disks separated by a 2.0 mm gap, and charged
  to 500 V.
a. Calculate the electric field strength (V = Ed)
b. Calculate the charge on each plate (E = Q/e0A)
c. A proton is shot through a hole in the negative
   plate towards the positive plate. It has an initial
   speed of 2.0 X 105 m/s. Does is have enough
   energy to reach the other side? (V = DPE/q)
                Electron Volt
• Energy an electron gains moving through a
  potential difference of 1 V
                 1 eV = 1.6 X 10-19 J

• Ex: An electron moving through 1000 V would
  gain 1000 eV of energy
     Voltage due to a Point Charge
• Voltage is not directional (scalar)
• Charged particles (i.e.: electrons, protons) have a
  voltage

V = kQ
     r
                   Example 1
Consider a +1.0 nC charge.
a. Calculate the electric potential (voltage) at a
   point 1.0 cm from the charge
b. Calculate the electric potential at a point 3.0 cm
   from the charge.
            Point Charges: Example 2
Calculate voltage (electric potential) at point A as
 shown below:
        A



30 cm




                      52 cm

   Q1 = +50 mC                         Q2 = -50 mC
Use Pythagoream theorem to calculate the distance
 from A to Q2:



        A



30 cm




                    52 cm

   Q1 = +50 mC                      Q2 = -50 mC
V A = V1 + V 2

V1 = kQ = (9.00X 109 Nm2/C2)(5.00X10-5C)
     r            (0.30 m)
V1 = 1.50 X 106 V
V1 = kQ = (9.00X 109 Nm2/C2)(-5.00X10-5C)
     r            (0.60 m)
V2 = -7.5 X 105 V

VA = 1.50 X 106 V -7.5 X 105 V
VA = 7.5 X 105 V
        Point Charges: Example 3
Calculate voltage (electric potential) at point B as
 shown below:
                         B




                     30 cm



          26 cm                    26 cm

   Q1 = +50 mC                         Q2 = -50 mC
Use Pythagoream theorem to calculate the distance
 from B to Q1 and to Q2:



                       B




                   30 cm



          26 cm                 26 cm

   Q1 = +50 mC                      Q2 = -50 mC
V A = V1 + V 2

V1 = kQ = (9.00X 109 Nm2/C2)(5.00X10-5C)
     r              (0.40 m)
V1 = 1.125 X 106 V
V1 = kQ = (9.00X 109 Nm2/C2)(-5.00X10-5C)
     r              (0.40 m)
V2 = -1.125 X 105 V

VA = 1.125 X 106 V –1.125 X 105 V
VA = 0 V
       Point Charges: Example 4
How much work is required to bring a charge of q =
 3.00 mC to a point 0.500 m from a charge Q =
 20.0 mC?

VQ = kQ   =     (9.00X 109 Nm2/C2)(2.00X10-5C)
      r                   (0.500 m)

VQ = 3.6 X 105 V (This is the voltage caused by
                    the stationary charge)
W = DU (like the work to lift a book to a shelf)
V = DU
     q
V=W
     q
W = Vq
W = (3.6 X 105 V )(3 X 10-6 C)
W = 1.08 J
       Point Charges: Example 5
Which of three sets of charges has the most:
• positive potential energy?
• The most negative potential energy?
• Would require the most work to separate?
                (i)
    +   -


                (ii)
+           -



                (iii)
+           +
              Charged Spheres
Act as point charges

At surface of sphere




Substitute:
A proton is released from rest at the surface of a
  1.00 cm-diameter sphere charged to +1000 V.
a. Calculate the charge on the sphere (0.56 nC)
b. Calculate the speed of the proton when it is 1.00
   cm from the sphere (note that it has potential
   energy in both cases, U = qV) (3.6 X105 m/s)
A thin ring has a radius R and charge Q. Find the
 potential at a distance of z from the axis of the
 ring.
A thin disk has a radius R and charge Q. Find the
 potential at a distance of z from the axis of the
 ring.
A 17.5 mm diameter dime is charged to +5.00 nC.
a. Calculate the potential of the dime (10,300 V)
b. Calculate the potential 1.00 cm above the dime
   (3870 V)