Download Electric Charges, Forces and Fields

Physics 202
Professor P. Q. Hung
311B, Physics Building
Physics 202 – p. 1/2
Electric Charges, Forces and Fields
http://galileo.phys.virginia.edu/~pqh/202/PHYS_
202_ homepage.htm
Physics 202 – p. 2/2
Electric Charges, Forces and Fields
http://galileo.phys.virginia.edu/~pqh/202/PHYS_
202_ homepage.htm
Important informations contained in the
homepage.
Physics 202 – p. 2/2
Electric Charges, Forces and Fields
A problem:
3 charges lie along the x-axis. Charge
q1 = 1µC is at the origin. Charge q2 = −3µC
is at x = −0.30m. Charge q3 = −4µC is at
x = +0.20m. Find the net electrostatic force
acting on q1 .
Physics 202 – p. 3/2
Electric Charges, Forces and Fields
A problem:
3 charges lie along the x-axis. Charge
q1 = 1µC is at the origin. Charge q2 = −3µC
is at x = −0.30m. Charge q3 = −4µC is at
x = +0.20m. Find the net electrostatic force
acting on q1 .
What is an electric charge? What is this
strange unit µC? What is the meaning of an
electrostatic force on one charge in the
presence of two other charges? Is it a contact
force or not?
Physics 202 – p. 3/2
Electric Charges, Forces and Fields
Electric charges
Electricity comes from the Greek elektron =
Amber.
Physics 202 – p. 4/2
Electric Charges, Forces and Fields
Electric charges
Electricity comes from the Greek elektron =
Amber.
Rub an amber rod and you can pick up little
pieces of papers, a phenomenon usually
referred to as “static electricity”.
⇒ The rod becomes “charged” by rubbing.
Physics 202 – p. 4/2
Electric Charges, Forces and Fields
Electric charges
Electricity comes from the Greek elektron =
Amber.
Rub an amber rod and you can pick up little
pieces of papers, a phenomenon usually
referred to as “static electricity”.
⇒ The rod becomes “charged” by rubbing.
You rub two amber rods and put them close
to each other: They repel each other.
Physics 202 – p. 4/2
Electric Charges, Forces and Fields
Electric charges
Electricity comes from the Greek elektron =
Amber.
Rub an amber rod and you can pick up little
pieces of papers, a phenomenon usually
referred to as “static electricity”.
⇒ The rod becomes “charged” by rubbing.
You rub two amber rods and put them close
to each other: They repel each other.
You rub two glass rods and put them close to
each other: They repel each other.
Physics 202 – p. 4/2
Electric Charges, Forces and Fields
Electric charges
You rub one amber rod and one glass rod and
put them close to each other: They attract
each other. ⇒ Two kinds of charges!
Physics 202 – p. 5/2
Electric Charges, Forces and Fields
Electric charges
You rub one amber rod and one glass rod and
put them close to each other: They attract
each other. ⇒ Two kinds of charges!
Like charges repel while unlike charges
attract.
Physics 202 – p. 5/2
Electric Charges, Forces and Fields
Electric charges
You rub one amber rod and one glass rod and
put them close to each other: They attract
each other. ⇒ Two kinds of charges!
Like charges repel while unlike charges
attract.
Benjamin Franklin: positive charge for the
rubbed glass rod and negative charge for the
rubbed amber rod. Arbitrary choice!
Physics 202 – p. 5/2
Electric Charges, Forces and Fields
Electric charges
Electric charge is conserved! If some positive
amount of charges is produced somewhere,
an equal amount of negative charge is also
produced.
Physics 202 – p. 6/2
Electric Charges, Forces and Fields
Electric charges
Electric charge is conserved! If some positive
amount of charges is produced somewhere,
an equal amount of negative charge is also
produced.
The unit of charge is C which stands for
Coulomb.
Physics 202 – p. 6/2
Electric Charges, Forces and Fields
Electric charges
Electric charge is conserved! If some positive
amount of charges is produced somewhere,
an equal amount of negative charge is also
produced.
The unit of charge is C which stands for
Coulomb.
Where do these charges come from? From
the atom!
Physics 202 – p. 6/2
Electric Charges, Forces and Fields
Electric charges: The Atom
Physics 202 – p. 7/2
Electric Charges, Forces and Fields
Electric charges
Atom: object with a nucleus (made out of
protons and neutrons) carrying a net positive
charge surrounded by electrons carrying a
net negative charge of the same magnitude.
Atoms are neutral.
Physics 202 – p. 8/2
Electric Charges, Forces and Fields
Electric charges
Atom: object with a nucleus (made out of
protons and neutrons) carrying a net positive
charge surrounded by electrons carrying a
net negative charge of the same magnitude.
Atoms are neutral.
The charge of the proton is
+|e| = 1.6 × 10−19 C and that of the electron is
−|e| = −1.6 × 10−19 C. That of the neutron is
zero. A neutral atom has an equal number of
protons and electrons.
Physics 202 – p. 8/2
Electric Charges, Forces and Fields
Electric charges
Charges can be exchanged by removing or
adding electrons.
Physics 202 – p. 9/2
Electric Charges, Forces and Fields
Electric charges
Charges can be exchanged by removing or
adding electrons.
A neutral atom with electrons removed ⇒ a
positive ion; added ⇒ a negative ion.
Physics 202 – p. 9/2
Electric Charges, Forces and Fields
Electric charges
Charges can be exchanged by removing or
adding electrons.
A neutral atom with electrons removed ⇒ a
positive ion; added ⇒ a negative ion.
Nucleus: positively-charged protons +
electrically neutral particles: neutrons.
Modern theory of particle physics: protons
and neutrons are made out of even smaller,
electrically charged particles: the quarks. We
are all made out of charged particles!
Physics 202 – p. 9/2
Electric Charges, Forces and Fields
How does a charged rod attract a neutral piece
of paper?
Physics 202 – p. 10/2
Electric Charges, Forces and Fields
Insulators and Conductors
Materials with electrons loosely bound to the
nuclei and which can “freely” move within ⇒
conductor. “Free” electrons: conduction
electrons. Examples are metals.
Physics 202 – p. 11/2
Electric Charges, Forces and Fields
Insulators and Conductors
Materials with electrons loosely bound to the
nuclei and which can “freely” move within ⇒
conductor. “Free” electrons: conduction
electrons. Examples are metals.
Materials with electrons very tightly bound to
the nuclei and which cannot freely move
about: insulators. Wood is an example.
Physics 202 – p. 11/2
Electric Charges, Forces and Fields
Insulators and Conductors
Materials with electrons loosely bound to the
nuclei and which can “freely” move within ⇒
conductor. “Free” electrons: conduction
electrons. Examples are metals.
Materials with electrons very tightly bound to
the nuclei and which cannot freely move
about: insulators. Wood is an example.
In between, materials with few conduction
electrons and which have interesting
properties: semiconductors. Silicon is an
example.
Physics 202 – p. 11/2
Electric Charges, Forces and Fields
Charging a Conductor
Physics 202 – p. 12/2
Electric Charges, Forces and Fields
Coulomb’s Law
Recall the attractive gravitational force
between two masses, m1 and m2 :
Fg =
m1 m2
−G r2
Physics 202 – p. 13/2
Electric Charges, Forces and Fields
Coulomb’s Law
Recall the attractive gravitational force
between two masses, m1 and m2 :
Fg =
m1 m2
−G r2
Experimental discovery by Coulomb:
Coulomb’s Law. Electrostatic force between
two point charges, q1 and q2 :
Fe =
q1 q2
k r2
2
(1)
k = 8.99 × 109 N.m2 /C . (1) is valid not just for
point charges but also for charge distributions
Physics 202 – p. 13/2
Electric Charges, Forces and Fields
Gravitational force vs Electrostatic force
The gravitational force is always attractive
while the electrostatic force can be attractive
or repulsive depending on the sign of the
product q1 q2 .
Physics 202 – p. 14/2
Electric Charges, Forces and Fields
Gravitational force vs Electrostatic force
The gravitational force is always attractive
while the electrostatic force can be attractive
or repulsive depending on the sign of the
product q1 q2 .
The electrostatic force is attractive when
q1 q2 < 0, i.e. the two charges have opposite
signs (one positive and the other one
negative).
Fe =
|q1 | |q2 |
−k r2
(1)
Physics 202 – p. 14/2
Electric Charges, Forces and Fields
Gravitational force vs Electrostatic force
The electrostatic force is repulsive when
q1 q2 > 0, i.e. the two charges have the same
signs (either both positive or both negative).
Fe =
|q1 | |q2 |
k r2
(1)
Physics 202 – p. 15/2
Electric Charges, Forces and Fields
Gravitational force vs Electrostatic force
The electrostatic force is repulsive when
q1 q2 > 0, i.e. the two charges have the same
signs (either both positive or both negative).
Fe =
|q1 | |q2 |
k r2
2
(1)
Since Fe goes like 1/r , the electrostatic force
becomes stronger for smaller distances and
vice versa. Strong bonding at short distances
for objects such as adhesive tapes.
Physics 202 – p. 15/2
Electric Charges, Forces and Fields
Coulomb’s Force is a vector
F~21 = k q1r2q2 r̂
where r̂ = ~r/r is the unit vector pointing from q1
to q2 . F~21 : Force on q2 due to q1 .
Physics 202 – p. 16/2
Electric Charges, Forces and Fields
Some examples
Physics 202 – p. 17/2
Electric Charges, Forces and Fields
A problem
3 charges lie along the x-axis. Charge q1 = 1µC
is at the origin. Charge q2 = −3µC is at
x = −0.30m. Charge q3 = −4µC is at
x = +0.20m. Find the net electrostatic force
acting on q1 .
Concept: Net force on q1 = Vector sum of the
electrostatic forces on q1 due to q2 and q3 ⇒
Superposition Principle.
Physics 202 – p. 18/2
Electric Charges, Forces and Fields
A problem
3 charges lie along the x-axis. Charge q1 = 1µC
is at the origin. Charge q2 = −3µC is at
x = −0.30m. Charge q3 = −4µC is at
x = +0.20m. Find the net electrostatic force
acting on q1 .
Concept: Net force on q1 = Vector sum of the
electrostatic forces on q1 due to q2 and q3 ⇒
Superposition Principle.
Draw a picture of the forces
Physics 202 – p. 18/2
Electric Charges, Forces and Fields
A problem: Solution
q1 q2 = −3(µC)2 = −3 × 10−12 C 2 is negative.
The force on q1 from q2 is attractive and points
in the negative x-direction (toward q2 ). Let the
unit vector pointing in the positive x-direction
be î. One obtains
9
2
2 3×10−12 C 2
~
F12 = −(8.99 × 10 N.m /C ) (0.30m)2 î =
−0.30 N î.
Physics 202 – p. 19/2
Electric Charges, Forces and Fields
A problem: Solution
Similarly, q1 q3 = −4(µC)2 = −4 × 10−12 C 2 is
negative. The force on q1 from q3 is attractive
and points in the positive x-direction (toward
q3 ). One obtains
9
2
2 4×10−12 C 2
~
F13 = (8.99×10 N.m /C ) (0.20m)2 î = 0.90 N î.
Physics 202 – p. 20/2
Electric Charges, Forces and Fields
A problem: Solution
The net force on q1 is
F~net = F~12 + F~13 = 0.60 N î
and points in the positive x-direction.
Physics 202 – p. 21/2
Electric Charges, Forces and Fields
A problem: Solution
The net force on q1 is
F~net = F~12 + F~13 = 0.60 N î
and points in the positive x-direction.
Summary: 1) Calculate each force
separately; 2) Sum the 2 forces as vectors to
get the final result.
Physics 202 – p. 21/2
Electric Charges, Forces and Fields
Coulomb’s Law: Charge distributions
Coulomb’s law also applies to charge
distribution: Same formula.
Physics 202 – p. 22/2
Electric Charges, Forces and Fields
Coulomb’s Law: Charge distributions
Coulomb’s law also applies to charge
distribution: Same formula.
Example: Charge distributed uniformly over
the volume of a sphere of radius R with a
volume charge density ρ ⇒ Total charge
Q = ρ( 43 πR3 ).
Physics 202 – p. 22/2
Electric Charges, Forces and Fields
Coulomb’s Law: Charge distributions
Coulomb’s law also applies to charge
distribution: Same formula.
Example: Charge distributed uniformly over
the volume of a sphere of radius R with a
volume charge density ρ ⇒ Total charge
Q = ρ( 43 πR3 ).
Electrostatic force between 2 such spheres:
F~e = k Q1r2Q2 r̂
Physics 202 – p. 22/2
Electric Charges, Forces and Fields
Electric field
Recall:
F~21 = k q1r2q2 r̂ (1)
Physics 202 – p. 23/2
Electric Charges, Forces and Fields
Electric field
Recall:
F~21 = k q1r2q2 r̂ (1)
Define an electric field due to q1 :
~
E(r)
= k q12 r̂
r
Physics 202 – p. 23/2
Electric Charges, Forces and Fields
Electric field
Recall:
F~21 = k q1r2q2 r̂ (1)
Define an electric field due to q1 :
~
E(r)
= k q12 r̂
r
Rewrite (1) as
~
(1)
F~21 = q2 E(r)
Physics 202 – p. 23/2
Electric Charges, Forces and Fields
Electric field
Recall:
F~21 = k q1r2q2 r̂ (1)
Define an electric field due to q1 :
~
E(r)
= k q12 r̂
r
Rewrite (1) as
~
(1)
F~21 = q2 E(r)
This is the force on q2 in the presence of an
~
electric field E(r)
Physics 202 – p. 23/2
Electric Charges, Forces and Fields
q
~
Electric field of point charge: E(r) = k r2 r̂
Physics 202 – p. 24/2
Electric Charges, Forces and Fields
Electric field: Example problem
Two positive point charges, q1 = +16µC and
q2 = +4µC, are separated in a vacuum by a
distance of 3.0m. Find the spot on the line
between the two charges where the net electric
field is zero.
The electric field is a vector.
Physics 202 – p. 25/2
Electric Charges, Forces and Fields
Electric field: Example problem
Two positive point charges, q1 = +16µC and
q2 = +4µC, are separated in a vacuum by a
distance of 3.0m. Find the spot on the line
between the two charges where the net electric
field is zero.
The electric field is a vector.
The net electric field is the vector sum of the
two individual electric fields.
Physics 202 – p. 25/2
Electric Charges, Forces and Fields
Electric field: Example problem
Since both charges are positive, the electric
fields coming from q1 and q2 at any point in
between will be pointing in the opposite
direction to each other. Therefore the net
electric field will be the difference of the two
individual electric fields.
Physics 202 – p. 26/2
Electric Charges, Forces and Fields
Electric field: Example problem
Let l be the distance from q1 of the point in
between where the two electric fields exactly
cancel each other, resulting in a zero net
electric field. One has
4µC
k 16µC
=
k
l2
(3.0m−l)2
4.0(3.0m − l)2 = l2
2.0(3.0m − l) = ±l
l = 2.0m; l = 6.0m
Only l = 2.0m is the correct answer (in
between point).
Physics 202 – p. 27/2