PHY 2049: Physics II Coulomb’s law,

electric field, Gauss’ theorem and electric potential.

-W = qΔV Energy

conservation applies.

F U

A u

nifo

rm e

lect

ric fi

eld,

with

a m

agni

tude

of 6

00 N

/C, i

s di

rect

ed p

aral

lel t

o th

e po

sitiv

e x-axis

. If t

he p

oten

tial a

t x =

3.0

m is

1 0

00 V

, wha

t is

the

pote

ntia

l at x

=

1.0

m? a.

400

Vb.

1 6

00 V

c. 2

200

Vd.

2 5

00 V

E V

qEF

xUF

qVU

xVE

PHY 2049: Class Quiz

If 500 J of work are required to carry a charged particle between two points with a potentialdifference of 20V, the magnitude of the charge on the particle is:

A. 0.040CB. 12.5CC. 20CD. cannot be computed unless the path is givenE. none of these

PHY 2049: Physics II

What is the potential at the center point (in units of kq/d) ?

a) -7 (b) -5 (c) -7 (d) -7

PHY 2049: Physics IICalculate the Electric Field at PCalculate the el. potential at P

dkqV

dkqE

dkqE

y

x

4

2232

221152

2

2

PHY 2049: Physics II

)(2

ln

22

22

zRz

ddllk

rqk

rqkV

o

i i

i

•Point charge

•Distribution of charges

•Line charge at an edge

•Disc on an axis through the center

Some old business:

What is the electric fieldof a shellof a uniform spherical charge distribution?

What is the potential for each of the above?

PHY 2049: Physics II Some old

businessThe potential of a

uniform spherical charge.

Calculate electric field, integrate it to get the potential

E

V

V

rR

Two particles with charges Q and -Q are fixed at the vertices of an equilateral triangle with sides of length a. The work required to move a particle with charge q from the other vertex to the center of the line joining the fixed particles is:

A. 0 B. kQq/a C. kQq/a2

D. 2kQq/a E. 1.4kQq/a

PHY 2049: Physics II a= 39 cm q1 = 3.4pC q2 = 6 pC E at the center? What is the

potential at the center?

6.26,6.1

8

21

2

akq

E

qakV

PHY 2049: Physics IIAn outline Capacitors, plate, coaxial, spherical.. Energy, Dielectric strength, Dielectric

constant. Netweorks: Parallel and Series

configuration.

PHY 2049: Physics II Capacitors: A device to hold charge.

It is held by Coulomb force between the charges. +q and –q on two separate places.

V : potential difference: q= CV C: capacitance units farad.

PHY 2049: Physics II

PHY 2049: Physics II

dAC

dEdV

o

o

Potential near a sheet charge

zV

ConstdzEzV

o

2

.)(

Potential near a sheet charge

dAC

dAQVV

zV

ConstdzEzV

o

o

o

/

.)(

PHY 2049: Physics II

PHY 2049: Physics II

)/ln(2

ln2

ln2

.

12

)(

abhCab

hQVV

r

drErV

rrE

o

oba

o

o

PHY 2049: Physics II

Rab

abC

bakqVV

rqkrV

rqkE

oo

ba

44

11

2

HITT A uniform electric field, with a

magnitude of 600 N/C, is directed parallel to the positive x-axis. If the potential at x = 3.0 m is 1000 V, what is the potential at x = 1.0 m?

 a. 400 V b. 1600 V c.

2200 Vd. 2500 V

PHY 2049: Physics II What is the capacitance of various

familiar balls.C = 4πεoR = 10-10 R(m) F

Basketball-it is an insulator Van de Graff top Earth (radius 6.4 X 106 m)

CE = 0.71 mF

PHY 2049: Physics II Energy stored in a capacitorU = ½ CV2 = Q2/2C = ½ QV Dielectric Strength (oops I burned it/broke it) Capacitor Enhancement by inserting a

dielectric:

Replace εo by κεo

PHY 2049: Physics II

PHY 2049: Physics II

Ceq = C1+C2+C3

PHY 2049: Physics II

321

1111CCCC eq

PHY 2049: Physics II Charging and discharging of

capacitors. http://edugen.wiley.com/edugen/

instructor/main.uni

PHY 2049: Physics II

25.20

PHY 2049: Physics IISwitch closed on left, capacitor C1 is being charged

CVVCQ 100101011 We have C2 = C3 = 20 μF in parallel. The equivalent capacitor is then Ceq = 40 μF. When the switch is thrown to right, the battery is disconnected, the charge is shared between the capacitors C1 and Ceq

= 40. What is the charge on old C2 and C3? Is your answer 40 μC? What is your answer if C2 = 10 μF and C3 = 30 μF?

.2,802',20'

100''

11

11

1

1

VoltsVCQVoltsVCQ

CQQCQ

CQ

VV

eqeq

eqeq

eq

eq

PHY 2049: Physics II All about capacitors Capacitance units Farad C = 4 π κεo R for a sphere of radius R

and dielectric constant κ. Energy stored dielectrics and strength Parallel and series elements in a

network