physics 152 walker, chapter 20 electrostatic potential energy electrostatic potential

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Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

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Page 1: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Physics 152Walker, Chapter 20

Electrostatic Potential Energy

Electrostatic Potential

Page 2: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 2

Electric Potential and Electric Potential Energy

Symbol for electric potential is V We will first define Electric Potential Energy. Symbol is UScalar quantity (a magnitude, positive or negative, not a direction) Unit is Joule (J).

Electric Potential Energy is an energy of a charged object in an external electric field.

Electric Potential is the property of the electric field itself, whether or not a charged object has been placed in it.

Page 3: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 3

The electrostatic force is a conservative force.Conservative because the force on a charge depends only on the

position of the charge, not its velocity or past trajectory.

We can define an electrical potential energy U (Joules) associated with the electrostatic force.

Electrical Energy Terms and Definitions

Page 4: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 4

As a charge q moves parallel (in same direction) to a constant electric field E, it experiences a force F=qE. The work done by the electric field is, W=Fd=qEd. (work is negative if force F and displacement d are in opposite directions)

The change in the potential energy is just the negative of the work done by the electric field:

U = - W = - qEd

Electrical Energy Terms and Definitions (continued)

Page 5: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 5

Change in electric potential energyMove the + particle opposite the direction of force = increase its potential

energy

Page 6: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 6

Question 1

• A positive charge moves from a) to b) in the electric field E. The work done by the electrostatic force is:

1) Positive

2) Negative

3) zero(b)

(a)

W = F(xf-xi)

Page 7: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 7

Question 2

• A positive charge moves from a) to b) in the electric field E. The change in the electrostatic potential energy is :

1) Positive

2) Negative

3) zero

(b)

(a)

U = Eq(xf-xi)

Page 8: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 8

A uniform electric field of magnitude 4.1x105 N/C points in the positive x direction. Find the change in electric potential energy of a +4.1 µC charge as it moves from the origin to (a) (0, 6.6 m) [ans:0], (b) (6.6 m, 0) [ans:-11.1], and (c) (6.6 m, 6.6 m) [ans:-11.1]

E

Walker P. #1

q

Page 9: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 9

It is often convenient to consider not the potential energy, but rather the potential difference between two points.

The potential difference between points A and B, (VB -VA ), is defined as the change in potential energy of a charge q moved from A to B divided by that charge

Potential is a scalar, NOT a vector.

uniform is E if ),( ABAB

ABAB

xxEVV

q

U

q

UUVVV

Electric Potential

Page 10: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 10

The potential V is measured in units of volts:

1 Volt = 1 V = 1 J /C = 1 N·m / C

With this definition of the volt, we can express the units of the electric field as:

[E]=1 N/C = 1 V/m

Note: potential (V) potential energy (U)

Unfortunately, we use V both for the electrostatic potential, and for its unit of measure, e.g. V(x1) = 2.5 V.

Units

Page 11: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 11

The zero of potential:For calculating physical quantities it is the difference in potential which has significance, not the potential itself. Therefore, we are free to choose as having zero potential at any arbitrary point which is convenient. Typical choices are:

• the earth• infinity, i.e. remotely far from the charges we are studying.

Electric Field, Electric Potential Energy, and Work

U = W = -Fd V = U/q = Ed

d

VE [1 N/C]=[1 V/m](uniform field)

Page 12: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 12

Energy Conservation

A consequence of the fact that electric force is conservative is that the total energy of an object is conserved

(as long as nonconserative forces such as friction can be ignored)

Expressing the kinetic energy:

BBAA UKUK

BBAA UmvUmv 22

2

1

2

1

qVU Electric potential energy is

Page 13: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 13

Point Charges

• If we define the zero of potential to be at infinity, then the potential at a point A which is a distance r from a point charge q is found to have a potential given by:

q Ar

r

q

r

qkVA

04

1

Electrostatic Potential

0

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1

Distance (m) from 0.1nC point charge

Vo

lts

(Dimensional analysis:E = kq/r2, V has dimensions of E times a length. r is the only length in the problem).

Page 14: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 14

Many Charges and Superposition

•If we wish to know the potential at a given point in space which results from all surrounding charges, we simply add up

the potential from each charge:

•Note that because potential is a scalar, the summation is less difficult than for the vector field E.

•If we have a continuous distribution of charge, we use techniques of integral calculus to calculate V(x,y,z).

...3

3

2

2

1

1 r

qk

r

qk

r

qkVA

Page 15: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 15

Potential and Work

For any group of charges, we can calculate the work done by the electrostatic force as the charges are brought together from infinity.

The potential energy associated with a two charge system:

r

qqkU 21

q1

q2

Page 16: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 16

Walker P. #33The three charges are held in place in the figure below, where L = 1.25 m. (a) Find the electric potential at point P [ans:76.9 kV] (b) Suppose that a fourth charge, with a charge of 6.11 C and a mass of 4.71 g, is released from rest at point P. What is the speed of the fourth charge when it has moved infinitely far away from the other three charges? [ans:14.1 m/s]

Page 17: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 17

It is often convenient to work with a unit of energy called the electron volt.

One electron volt is defined as the amount of energy an electron (with charge e) gains when accelerated through a potential difference of 1 V:

1 eV = (1.6 · 10-19 C)V= 1.6 · 10-19 J

The Electron Volt (eV)

A Battery is an electron pump. A battery (1.5 V), each electron pumped through the battery from + to - is given a potential energy of 1.5eV.

Page 18: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 18

A (real or imaginary) surface in space for which the potential is the same everywhere is called an equipotential surface.

• The electric field at every point on an equipotential surface is perpendicular to the surface.

• Equipotential surfaces are like contour lines on a topographic map.

Equipotential Surfaces

Page 19: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 19

Electric Field Lines and Equipotential Surfaces for two point charges

(Electric field lines and Equipotential surfaces are always mutually perpendicular).

Page 20: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 20

Q Q

A capacitor is device that stores the energy associated with a configuration of charges.

In general, a capacitor consists of 2 conductors, one with a charge +Q and the other with a charge –Q (on the surfaces). Any geometry is a capacitor

Capacitance

+++++

-

Page 21: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 21

• The capacitance C is defined as the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between the conductors:

For parallel plate C = A 0 /d. (C does not depend on Q or V)

[V = Ed, E=Q/(A 0), V = Qd / (A 0)]

The unit of capacitance is the Farad (F): 1 F = 1 C/V

V

QC

Page 22: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 22

The Parallel-plate CapacitorA common type of capacitor is the parallel-plate capacitor, made up simply of two flat plates of area A separated by a distance d. Its capacitance is given by:

where 0 is a constant called the permittivity of free space.

d

AC 0

0=8.8510-12 C2 / Nm2

04

1

k

Page 23: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 23

A dielectric is an insulating material in which the individual molecules polarize in proportion to the strength of an external electric field. This reduces the electric field inside the dielectric by a factor , called the dielectric constant.

0CC

Capacitance is increased by .

0E

E 0V

V and

Dielectrics

For fixed charge Q on plates

Page 24: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 24

Dielectric Strength

• Dielectrics are insulators: charges are not free to move (beyond molecular distances)

• Above a critical electric field strength, however, the electrostatic forces polarizing the molecules are so strong that electrons are torn free and charge flows.

• This is called Dielectric Breakdown, and can disturb the mechanical structure of the material

Page 25: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 25

Dielectric Properties of common materials

Material Dielectric Constant:

Dielectric Strength (V/m)

Vacuum 1 2.5·1018

Air (lightening) 1.00059

(-1) Density

3.0·106

Teflon 2.1 60 ·106

Paper 3.7 16 ·106 Mica 5.4 100 ·106

Page 26: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 26

Energy Stored in a Capacitor

Recall that work is required to move charges about or “charge” the capacitor. The work required to charge a capacitor with a charge q to a voltage V is:

So this must correspond to the energy stored in the capacitor. Because Q=CV, this can be rewritten:

QV2

1E

C

QCV

22

1 22 E

Page 27: Physics 152 Walker, Chapter 20 Electrostatic Potential Energy Electrostatic Potential

Walker Chapter 20 27

Walker P. #50(a) What plate area is required if an air-filled, parallel-plate capacitor with a plate separation of 2.8 mm is to have a capacitance of 26 pF? [ans:0.00822 m2]

(b) What is the maximum voltage that can be applied to this capacitor without causing dielectric breakdown? [ans:8.4 kV]