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Chapter 29. Electric Potential and Field. Overview Force, field, energy, potential. Force, field, energy, potential. or. Fields and potentials. - PowerPoint PPT Presentation
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Fields and potentials
Phys 133 – Chapter 29 4
1. a) E = 0 V/m in throughout some region of space, can you conclude that the potential V = 0 in this region?
b) V = 0 V throughout some region of space. Can you conclude that the electric field E = 0 V/m in this region?
Phys 133 – Chapter 29 5
Graphically convert between E and V
2. The top graph shows Ex vs. x for an electric field parallel to the x-axis.a) Draw the graph of V vs. x in this region of space. Let V = 0 at x = 0m. Add an appropriate scale on the vertical axis. (Hint: integration is the area under the curve)
b) Draw a contour map above the x-axis on a diagram like the one below-right and label your equipotential lines every 20 V. 0V has been drawn already.
C) Draw several electric field vectors on top of the contour map.
2 4
20
40
Ex (V/m)
1 20 3 4
x(m)x(m)
0 V
Phys 133 – Chapter 29 6
--Find the electric potential everywhere for a sphere (radius R) with charge (Q) uniformly distributed. Take V=0 at infinity.
--Sketch V vs r and Er vs r.
From Chap 27 E field is:
Problem: Potential of sphere
Phys 133 -- Chapter 30 7
Problem: Potential of sphere (ans)
rdefinition
For all r
For R < r
Vr V∞
∆VFinding Vr
For r < RVr
Vr
VR
∆V
Phys 133 – Chapter 29 8
Find the electric potential everywhere for a sphere (radius R) with charge (Q) uniformly distributed.
Problem: Potential of sphere (ans)
Phys 133 – Chapter 29 9
Find the x,y and z components of the electric field, given that the electric potential of a disk is given by
Problem: Field from Potential
Phys 133 – Chapter 29 10
Find the z component of the electric field, given that the electric potential of a disk is given by
Problem: Field from Potential (Answer)
Phys 133 – Chapter 29 11
is perp to equipotential surfaces
points downhill (decreasing V)
--strength proportional to spacing equipotentials
Geometry of potential/field
Phys 133 – Chapter 29 13
--field is zero inside conductor
--field is perpendicular at surface
--conductor is at equipotential (no work to move)
Conductor in equilibrium: field and potential
Phys 133 – Chapter 29 14
--equipotentials are parallel
to nearby conductor
Conductor in equilibrium: equipotentials
Phys 133 – Chapter 29 16
--Find the electric potential everywhere for a point charge (q) at the center of a hollow metal sphere (inner radius a, outer radius b) with charge Q. (Take V=0 at infinity.)
--Sketch V vs r and Er vs r.
Problem: Finding Potential
Phys 133 -- Chapter 30 17
Problem: Finding Potential (ans)
r
Vr V∞
∆V
Vr
Va
∆V
For all r
For b < r
Finding Vr
For a < r < b
For r < a
Phys 133 -- Chapter 30 22
--generic circuit elements
--imagine battery connection
parallel
series
Circuit geometry
Phys 133 -- Chapter 30 28
--Find the charge on (Q) and potential difference (V) across each capacitor.
--What is the total energy stored in the system?
Problem
Dielectrics change the potential difference
• The potential between to parallel plates of a capacitor changes when the material between the plates changes. It does not matter if the plates are rolled into a tube as they are in Figure 24.13 or if they are flat as shown in Figure 24.14.
Field lines as dielectrics change• Moving from part (a) to
part (b) of Figure 24.15 shows the change induced by the dielectric.
In dielectric
In vacuum, energy density is
Examples to consider, capacitors with and without dielectrics
• If capacitor is disconnected from circuit, inserting a dielectric changes decreases electric field, potential and increases capacitance, but the amount of charge on the capacitor is unchanged.
• If the capacitor is hooked up to a power supply with constant voltage, the voltage must remain the same, but capacitance and charge increase
You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the charges on the plates remain constant.
What effect does adding the dielectric have on the potential difference between the capacitor plates?
A. The potential difference increases.
B. The potential difference remains the same.
C. The potential difference decreases.
D. not enough information given to decide
Q24.8
You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the charges on the plates remain constant.
What effect does adding the dielectric have on the potential difference between the capacitor plates?
A. The potential difference increases.
B. The potential difference remains the same.
C. The potential difference decreases.
D. not enough information given to decide
A24.8
You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the charges on the plates remain constant.
What effect does adding the dielectric have on the energy stored in the capacitor?
A. The stored energy increases.
B. The stored energy remains the same.
C. The stored energy decreases.
D. not enough information given to decide
Q24.9
You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the charges on the plates remain constant.
What effect does adding the dielectric have on the energy stored in the capacitor?
A. The stored energy increases.
B. The stored energy remains the same.
C. The stored energy decreases.
D. not enough information given to decide
A24.9
You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the potential difference between the plates remains constant.
What effect does adding the dielectric have on the amount of charge on each of the capacitor plates?
A. The amount of charge increases.
B. The amount of charge remains the same.
C. The amount of charge decreases.
D. not enough information given to decide
Q24.10
You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the potential difference between the plates remains constant.
What effect does adding the dielectric have on the amount of charge on each of the capacitor plates?
A. The amount of charge increases.
B. The amount of charge remains the same.
C. The amount of charge decreases.
D. not enough information given to decide
A24.10
You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the potential difference between the plates remains constant.
What effect does adding the dielectric have on the energy stored in the capacitor?
A. The stored energy increases.
B. The stored energy remains the same.
C. The stored energy decreases.
D. not enough information given to decide
Q24.11
You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the potential difference between the plates remains constant.
What effect does adding the dielectric have on the energy stored in the capacitor?
A. The stored energy increases.
B. The stored energy remains the same.
C. The stored energy decreases.
D. not enough information given to decide
A24.11
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