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Electric Potential-Applied Physics-Lecture Slides, Slides of Applied Chemistry

This course includes Motion, Oscillations, waves and propagation, Electric Charge and Coulomb Law, Electric Field, Electric Potential, Capacitors and Dielectric, Current and Resistance, AC and DC, Magnetic fields, Ampere Law and Faraday law, Maxwell equations and Traveling waves. This file includes: Electrostatic, Gravitational, Force, Electric, Potential, Point, Charges, Field, Vector, Energy, Forces

Typology: Slides

2011/2012

Uploaded on 07/31/2012

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Electric Potential
Electrostatic and Gravitational force
Electric Potential Energy (EPE)
Electric Potential
Potential due to Point Charges
Calculating the Potential from the Field
Calculating the Field from Potential
Equipotential Surface
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Download Electric Potential-Applied Physics-Lecture Slides and more Slides Applied Chemistry in PDF only on Docsity!

1

Electric Potential  Electrostatic and Gravitational force

 Electric Potential Energy (EPE)

 Electric Potential

 Potential due to Point Charges

 Calculating the Potential from the Field

 Calculating the Field from Potential

 Equipotential Surface

2

Introduction

 Force is a vector and energy is scalar

 In problem involving vector forces and fields

 Calculations require sums and integral are often completed

 In this chapter we will study

 The energy method for electrostatics field

 we will start with the electric potential energy

 It is a scalar and will characterize an electrostatic force

4

The difference in potential energy between two points is equal to the negative of Work done by a force ΔU = - Wab

Above equation is possible only for conservative forces Which means that potential energy can only be defined for conservative forces

Forces are conservative if and only if the work done by these forces when a body moves from a to b is independent of the path taken between these two locations

5

For example work done by a force in the gravitational field is independent of the path followed by the particle

III

b

a II

I

We can make a similar argument for the electrostatic force with the same result

Which means that the electrostatic force is also conservative and can be demonstrated by potential energy

The only difference between the two is that gravitational force is only attractive and electrostatic force can be attractive and repulsive both

7

Consider system of two positive charges +q and q 0

The charge q 0 moves under the influence of E field created by +q

The charge q 0 moves a small displacement dr as it moves from position A to position B

Electric Potential Energy +++++++++++++ q

qo

A qo

B

rB Δr

rA

8

+++++++++++++ q

qo

A qo

B

rB Δr

rA

Magnitude of E field created by +q decreases as the charge q 0 moves farther away from charge +q

The charge q 0 experiences a force (F = q 0 E ) that varies with displacement

We need to calculate work done by a variable force

10

Work done by F = q 0 E WAB = EPEA EPEB

+q rA A

B F = q 0 E

q 0

q 0

F = q 0 E

+++++++++++++

rB

Electric Potential Energy

WAB = EPEA - EPE B

A B

AB

r

kq q

r

kq q

W =^0 -^0

B

A

B

A

AB

r

kq q

r

dr

W kq q

= (^0)  2 = 0 1

A B

AB

r r

W kq q

11

Work done by F = q 0 E WAB = EPEA EPEB

+q rA q 0

q 0

+++++++++++++

rB

Note that the above work must be related to change in Electric Potential Energy

EPE = U = Uf – Ui

Electric Potential Energy

A B

AB

r

kq q

r

kq q

W =^0 -^0

r A

kq 0 q

r B

kq 0 q

F = q 0 E

AB B A

W

r

kq q

r

kq q

 U =^0 -^0 = -

13

Work done by F = q 0 E WAB = EPEA EPEB

+q rA A

B F = q 0 E

q 0

q 0

F = q 0 E

+++++++++++++

In the above equation rA rB is the initial separation between the charges and rB is the final separation

Electric Potential Energy

B r A

kq q

r

kq q

 U =^0 -^0

final r initial

kq q

r

kq q

 U =^0 -^0

14

Electric Potential Energy

+++++++++++++^ +q Let us assume that the charge q 0 was at an infinite distance from this system

rintial = 

0

final r initial

kq q

r

kq q

 U =^0 -^0

final r initial

kq q

r

kq q

 U =^0 -^0

16

+q q 0

q 0

+++++++++++++

The EPE is only depend upon the^ r distance between the two positive charges and will be different if we place q 0 at different separation r

Remember that EPE is a scalar quantity

Where is the magnitude of E Also field at a distance r from q

Electric Potential Energy

(1) r

kq U(r)

q = 0

U =^ r E q 0 E

17

(1) r

kqq U(r) =^

0

 If the electric force is attractive, q and qo have opposite signs, and so the product qqo is negative, the electric potential energy given in equation will be negative

 If the electric force is repulsive, q and qo have the same sign, and the product qqo is positive, the electric potential energy is positive.

 If we move qo toward q (source charge) from an initially infinite separation, the potential energy increases from its initial value, which we have consider as zero.

19

Now we bring another charge q 2 from infinity

q (^1) r q 2 12

Electric Potential Energy of a System of Charges

12

1 2 r

kq q U =

20

And now we bring another charge q 3 from

infinity q 3

q 1 q 2

r 23

r 13

r 12

Electric Potential Energy of a System of Charges

23

2 3

13

1 3

12

1 2 r

kq q

r

kq q

r

kq q U = + +