Electric forces

1
Electric forces fields

• PHY232
• Remco Zegers
• zegers_at_nscl.msu.edu
• Room W109 cyclotron building
• http//www.nscl.msu.edu/zegers/phy232.html
• walk-in hours 430-530 pm Thu BPS 1248
  (helproom)

2
Resources for PHY232

• www.nscl.msu.edu/zegers/phy232.html
• syllabus
• lectures (pre and post lecture notes)
• old exams
• helproom hours
• exam homework schedule
• grading
• homework is done in LON-CAPA
• HITT clickers are used for extra credit
• extra credit quizzes start week 3
• 1 point for trying, 2 for correct answer
• need to enroll in LON-CAPA
• will use clicker frequently

3
Suggestions for studying

• for each chapter make an overview (1-2 pages)
  based on the
• lecture notes and textbook. Do not only
  include equations, but also
• main conceptual points. Try not to fall
  behind.
• after making the overview, start doing the
  lon-capa, using just the overview.
• if you cant do a problem using the overview,
  refer back to the lectures/book and update your
  overview
• use the guide for doing the homework problems
  provided in the lectures to cut down on the time
  to start a problem.
• if you get stuck (or it takes long to get started
  with a problem), go to the helproom or use the
  comments from others in lon-capa (but make sure
  to try yourself first!).
• The helproom is not only for homework go with
  broader questions as well.

4
suggestions II

• by the time an exam comes, you have good and
  tested overviews of each chapter which you can
  use to make your equation sheet.
• test for weaknesses with the old exams/review
  problems/book problems. Review the lon-capa.
• if you have trouble with units/conversions/math
  etc add to your equation sheet.
• memorizing lon-capa problems will likely not get
  you very far.
• If you feel that your efforts are not paying off
  (spending a lot of time but get poor scores),
  contact me. Dont wait until late in the
  semester.
• phy232 is a bit different from phy231 or
  equivalent course in the sense that the concepts
  are harder to visualize.

5
electric charges

• There are 2 types of charges
• positive (basic carrier proton)
• negative (basic carrier electron)
• In atoms, the nucleus consists of
• protons (positive)
• neutrons (neutral)
• And is surrounded by a cloud of electrons
  (negative)
• If the atom is not ionized, it is neutral.
• By removing electrons, it becomes ionized and
  positively charged, since there are more protons
  than electrons
• Note that the mass of the electron is much
  smaller than that of the proton and neutron
• me9.1093826x10-31 kg mp1.67262171x10-27 kg

6
question

• A neutral atom has
• more neutrons than protons
• more protons than electrons
• the same number of neutrons and protons
• the same number of protons and electrons
• the same number of neutrons, electrons and protons

• answer d)
• The protons have positive charge.
• The electrons have negative charge
• The neutrons are neutral.
• The total charge of an atoms is thus
• eNprotons -eNelectrons
• For this to be zero, NprotonsNelectrons

7
Charged objects

• Like charges repel each other

-
-

• Unlike charges attract each other

-

8
Conservation of charge

• In a closed system, charge is conserved. This
  means that charge is not created but rather
  transferred from one object to another.
• Charge is quantized there are only discrete
  amounts of charge. The electron carries one unit
  of negative charge (-e) and the proton carries
  one unit of positive charge (e).
  1e1.60219x10-19 C (Coulomb)

9
conductors

• In conductors (I.e. consisting of conducting
  materials) electric charge can move freely. The
  resistivity against the flow of charge is very
  small
• example metals e.g. Copper one of the electrons
  can move freely.

10
insulators semiconductors

• In insulators, charge can not move freely. The
  resistivity against the flow of charge is very
  high
• Semiconductors are materials whose properties are
  in between that of conductors and insulators.
• What makes a material a conductor/insulator?
• Depends on the shell structure of the atoms
  involved. We will discuss this later!

demo charge through air!
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charging by conduction
demo transferring charge

• An object can be charged by conduction

-



-


-
-






-

charged
neutral
charge is induced but object is still neutral

-
-




-



-





-


charged
neutral





contact





charged
charged
charge has moved by conduction
12
charging by induction

charge is induced object is still neutral
but polarized
-
-




-



-





-


charged
neutral
excess charge can escape

-
-




-



-

connected to earth




-


charged
neutral
-
demos bending water obedient ruler etc

-



-
-
-






- charged
charged
The earth is an infinite sink/source of electrons
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question
-
A
B
-
A
B

• a large negatively charged block is placed on an
  insulated table. A neutral metal ball (A) is
  rolled towards it and stops before it hits the
  block. Then, a second neutral metal ball (B) is
  rolled towards ball (A). After the collision,
  ball A stops closer to the block (but without
  touching) and ball B stops further away from the
  block. The block is then removed. What is the
  final charge on balls A and B?
• Ball A is positive, ball B is negative
• Ball A is negative, ball B is positive
• Both ball remain neutral
• Both balls are positive

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answer
15
Coulombs law - 1785

• Coulombs law
• directed along the line joining the two objects
• is attractive if the charges have the opposite
  sign
• is repulsive if the charge if the same sign
• ke Coulomb constant8.9875x109 Nm2/C2
• ?01/(4 ?ke)8.85x10-12 C2/(Nm2)
• to be used later

16
superposition principle

• When more than 1 charge acts on the charge of
  interest, each exerts an electric force. Each can
  be computed separately and then added as vectors
• in this case F13 and F23 are along the same line
  and can be added as number, but be careful with
  the sign!
• example q11nC, q22nC, q3-2nC, what is the net
  force on q3 ? r13r231m

r13
r23
F13
F23
q1
q2
-q3
Add
F138.99E9 x 1E-9 x 2E-9/121.8E-08 N (to the
left) F238.99E9 x 2E-9 x 2E-9/123.6E-08 N (to
the right) Net force 1.8E-08 N (to the right)
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superposition principle II

• Remember forces are vectors, so treat them
  accordingly!

-q3
r13
r23
F23
q2
F13
F3
q1
Add In this case, you need to take into
account the horizontal and vertical directions
separately and then combine them to get the
resultant force (I.e. like parabolic motion)
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questions true false
A
C
B

• if A and C are positive, B is pushed away from A
  and C
• if A and B are positive, A and B will move
  further apart
• if A is neutral and C is positive, B will move
  along the line BC
• if A,B and C have the same charge, they will
  separate further

• answers
• false, if B is negative it will move towards A
  and C
• false, if C is negative and the absolute charge
  much larger than A and B, A and B could come
  closer
• false, B might be neutral and not move at all
• true, they will all feel an outward pointing force

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lon-capa
F14
4
F24
F34
3
F54
5
1
2
do LC problems 1,3,4,10,12
20
a simple electroscope
useful for LC9
demo

• Two equal masses are charged positively (both 1
  ?C) and hung from massless ropes. They separate
  as shown in the figure. What is the mass of each?

1 m
0.01 m
tan?0.01/1Fe/Fg Fekeq1q2/r122 (coulomb
force) Fgmg9.81m (gravitational force) with
q1q2q and r1220.010.02 m, k8.99x109
Nm2/C2 so mFe/(0.01g)keq2/(0.01gr122) m229
kg !!!! The electric force is very strong
compared to the grav. force! Compare FgGm1m2/r12
2 with G6.67x10-11 Nm2/kg2 Fekeq1q2/r122 with
ke8.99x109 Nm2/C2
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gravitational electrical force

• two objects of mass 10 kg are placed 1 meter from
  each other. Each has 1x1010 excess electrons.
  What is the net force on each of the objects?

answer Fekeq1q2/r122 with ke8.99x109
Nm2/C2 1010 electrons 1010 x 1.6e-19 C1.6E-9 C
q1q2 Fe8.99x109 x (1.6E-9)2/12 2.30E-8
N FgGm1m2/r122 with G6.67x10-11 Nm2/kg2
6.67x10-11 x 102/12 6.67E-9 N Fe-Fg1.6E-8 N
(electric force is strong, so force is repulsive)
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loncapa

• do problem 11

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electric fields

• Instead of a force acting on an object A by an
  object B somehow magically over the distance
  between them, one can consider that object A is
  situated in a field arising from the presence of
  object B.
• Because object A is in the field created by
  object B, it feels a force
• The electric field produced by a charge Q at the
  location of a small test charge q0 is defined as

The magnitude of E only depends on the charge of
Q and not the sign and size of the test charge
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electric fields II

• electric fields and forces due to a charge Q on
  test charges of different charge and at different
  distances

Q
rc
C
rb
q0
ra
B
q0
A
-q0
rarbr rc2 x r
means pointing away from Q
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electric fields III

• To determine the electric field at a certain
  point 3, due to the presence of two other charges
  1 and 2, use the superposition principle.

q3
r13
r23
E23
-q2
E13
E3
-q1
E3 is independent of the charge q3 The field
would also be present if q3 were not there Note
that in this case F13 and F23 point in the
opposite direction of E13 and E12.
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question

• 2 charges equal in magnitude are lined up as
  shown in the figures. A third point (no charge) P
  is defined as well. In which case is the
  magnitude of the electric field at P largest? The
  distance between neighboring points is constant.

P


P

-
P

-
P
A
B
C
D
C is correct
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electric field lines

• To visualize electric fields, one can draw field
  lines that point in the direction of the field at
  any point following the following rules
• The electric field vector E is tangent to the
  electrical field lines at each point
• The number of lines per unit area through a
  surface perpendicular to the lines is
  proportional to the field strength
• field lines start from a positive charge
• field lines end at a negative charge
• field lines never cross

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electric field lines II

• Following these rules one can draw the field
  lines for any system of charged objects

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electric field lines II

• examples

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questions
P
Q
R

• charge P is a) positive b) negative
• charge Q is a) positive b) negative
• charge P is a) larger b) smaller than charge Q
• a negative charge at R would move a) toward P
• b) away from P c) toward Q

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lon-capa
do problems 6,7,8,9
32
conductors

• In the absence of any external charges, an
  insulated conductor is in equilibrium, which
  means
• the electric field is zero everywhere in the
  conductor
• since net field would result in motion of charge
• excess charge resides on the surface
• since electric force 1/r2 excess charge is
  repelled
• the field just outside the conductor is
  perpendicular to the surface
• otherwise charge would move over the surface
• charge accumulates where the curvature of the
  surface is smallest
• charges move apart more at flatter surfaces

33
Millikan oil-drop experiment I
No E-field (battery off) mgkv k drag constant
(known) so mkv/g

• Consider first the case where the battery was
  switched off.
• Oil droplets will fall and reach a constant
  velocity v which
• can be measured.
• At this velocity, the gravitational force
  balances the
• frictional (drag) force which equals kdragx
  velocity.
• From this the mass of the droplet can be
  determined.
• Now the E-field is switched on

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Millikans oil drop experiment II
E
The droplets are negatively charged. By tuning E
one can suspend them in air. If that happens the
electrical force balances the gravitational
force and qEmg. Millikan found qmg/En 1.6E-19
and thus discovered that charge was
quantized Nobel prize 1923!
35
Electric flux

• The number of field lines (N) through a surface
  (A) is proportional to the electric field NEA
• The flux ?EA (Nm2/C)
• If the field lines make an angle with the
  surface
• ?EAcos? where ? is the angle between the field
  lines and the normal to the surface
• For field lines going through a closed surface
  (like a sphere), field lines entering the
  interior are negative and those leaving the
  interior are positive

36
Gauss Law

• Consider a point charge q. Imagine a sphere with
  radius r surrounding the charge. The E-field and
  flux anywhere on the sphere are
• It can be proven that this holds for any closed
  surface
• Gauss Law

37
E-field inside/outside a sphere
charge on sphere Q
B
A
Faradays cage

• consider imaginary surface A
• ?Qinside/?00EA so, E0 (no field inside
  charged sphere)
• consider imaginary surface B
• ?Qinside/?0Q/ ?0EA so,
• EQ/(?0A) (net field outside charged
  sphere)

38
question
A point charge q is located at the center of a
spherical shell with radius a and charge q
uniformly distributed over its surface. What is
the E-field a) anywhere outside the shell and b)
at a point inside the shell at distance r
from the center.
-

• draw a Gaussian surface around the sphere and
  apply Gauss Law EQinside/(?A)0 since
  Qinsideq-q0
• draw a Gaussian surface around the q charge, but
  inside the shell at distance r from q and apply
  Gauss Law
• EQinside/(?A) -q/(?0 4?r2)-keq/r2 I.e.
  field points inward

39
question
A point charge q is located at the center of a
spherical shell with radius a and charge 2q
uniformly distributed over its surface. What is
the E-field a) anywhere outside the shell and b)
how much charge resides on the inner and outer
surface of the shell?
-

• draw a Gaussian surface around the sphere and
  apply Gauss Law EQinside/(?A)-q/(?A) since
  Qinside-q2qq
• inner surface charge much balance the charge
  placed in the center (-q) so q. The remainder
  of the charge wants to move away as far as
  possible outer surface (q). No charge is
  present in the shell.

40
question

• A neutral object A is placed at a distance r0.01
  m away from a charge B of 1?C.
• What is the electric field at point A?
• What is the electric force on object A?
• What is the flux through the sphere around object
  B that has a radius r0.01?
• A is replaced by a charge (object C) of 1 ?C.
  What is the force on C?
• What is the force on B?

• EkqB/rAB28.99x109 x 1x10-6 / 0.01289.9x106 N/C
• FEqA0
• ?EA 89.9x106 x (4?0.012)113x106 Nm2/C
• FEqA89.9x106 x 1x10-689.9 N (towards B)
• Same, but pointed towards A

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lon-capa
do problem 13