Some ways to charge objects
•By rubbing dissimilar
objects
•By chemical
processes
•By proximity between a
charge and a conductor –
charging by induction
•By physical contact
between a charge and
a conductor
+
+
-
Coulomb’s Law
•Like charges repel, unlike charges attract
•Force is directly along a line joining the two charges
q1
q2
r
Fe =
keq1q 2
r2
k e = 8.988×109 N⋅m2/C2
•An inverse square law, just like gravity
•Can be attractive or repulsive – unlike gravity
•Constant is enormous compared to gravity
Coulomb’s Law: Applied
A Helium nucleus (charge +2e) is separated from one of its
electrons (charge –e) by about 3.00 × 10-11 m. What is the force the
nucleus exerts on the electron? Is it attractive or repulsive?
Fe =
keq1q 2
k e = 8.988×109 N⋅m2/C2
r2
r = just
3.00calculated
× 10-11 m the force
We
q1 =on
3.204
the electron
× 10-19 Cfrom the
nucleus. How does this
q2 =compare
-1.602 ×with
10-19the
C force
on the nucleus from the electron?
A)
on the
nucleus is twice as big
F =The- force
0.513
µN
Attractive Force
B)e The force on the nucleus is half as big
C) The forces are equal in magnitude
1
Coulomb’s Law: Sample problem
Three charges are placed on a plane as shown: What are the
forces?
q2
R
q1
R
R
q3
Coulomb’s Law vs. Gravity
A Helium nucleus (charge +2e) is separated from one of its
electrons (charge –e) by about 3.00 × 10-11 m, and we just
calculated the electrostatic forces involved.
Fe =
keq1q 2
k e = 8.988×109 N⋅m2/C2
r2
Suppose we could adjust the distance between the
nucleus (considered as a point particle) and one
electron. Can we find a point at which the
electric and gravitational forces are equal?
A) Yes, move the particles apart.
B) Yes, move the particles together.
C) No, they will never be equal.
Quiz
Three
are suspended
from from
thin threads.
Various
Threeballs
pithballs
are suspended
thin threads.
Objects
then rubbed
objects
Variousare
Objects
are thenagainst
rubbedother
against
other
(nylon
glass
against
objectsagainst
(nylonsilk,
against
silk,
glasspolyester,
against etc.)
and
each
of
the
balls
is
charged
by
touching
polyester, etc.) and each of the balls is charged
them
with onethem
of these
It is found
by touching
with objects.
one of these
objects.that
It is
balls
and pithballs
2 repel each
other
and that
found1 that
1 and
2 repel
eachballs
other2and
and
repel each
other.
that3pithballs
2 and
3 repel each other.
From
Fromthis
thiswe
wecan
canconclude
concludethat:
that:
A)
1 and
carrycharges
chargesofofthe
opposite
sign.
B) Balls
All the
balls3carry
same sign
B)
All theofballs
sign
Charges
equalcarry
sign charges
repel, soof1 the
andsame
2 have
the
C) One
carries
charge.
sameball
sign,
as dono2 and
3, and so they all have the
D) Impossible
same sign.to determine without more
information.
2
Coulomb’s Law – more versions
r kqq
Fe = e 12 2 rˆ
r
•Force is a vector
(remember from last semester)
r
qq
Fe = 1 2 2 rˆ ε 0 = 8.854×10 -12 C2/ (N? m2)
4πε 0 r
•Permittivity of free space
Conductors redistribute charge
•Conductor
Q
Add charges,
Q
•Conductors allow free flow of
charge
•Like charges repel
•So the charges will redistribute
themselves over the sphere
Spherical Shells
•Just like with gravity, a charge
outside feels the charge from the
sphere as if it were concentrated
in the middle
Q
q
•Consider the forces from
opposite charge elements and the
vector decomposition
3
Coulomb’s Law
My body contains about 3×1028 electrons, all repelling each other.
How come I don’t explode?
A) Electrons attract each other, not repel each other
B) The gravitational force is so strong it holds me together,
overcoming electric forces
C) There are also positive charges that cancel out the negative
charges
D) Electrical forces are too weak to consider
4