ELECTRIC CHARGES
AND
FIELDS
GLIMPSES
Electrostatics is the
study
of
electric
charges
at
rest.
Only
electric field
is
associated
with
stationary
charges.
Electric charge (Scalar : SI
Unit
C)
Intrinsic property
of
elementary particles which
provides electric force between objects.
Basic
properties
of
charges
1.
Addivity : q =
4,
+
42
2.
Quantisation : q =
ne,
n =
0,
± 1, ±
2,
...
3.
Conservation : Total charge of
an
isolated
system remains constant.
4.
Like charges repel
and
unlike charges attract.
5. Speed has
no
effect on the charge of a body.
Basic
quantum
of
charge
It is the charge
on
an
electron
or
proton.
e=
1.602182 x
10
~
~
~
C
Coulomb's
law
The
force
of attraction
or
repulsion between two
stationary
point
charges separated
by
distance
~
in
free
space is
1
4112
47€.
1 2
0
0 permittivity of free space
=8.854 x
10
~
~
~
CN
'm
Permittivity
I Electric field (Vector : SI
unit
NC
~
)
Electrostatic force acting per unit test charge.
E Force F
Charge q
Electric field
of
a
point
charge
At
distance r from charge
q,
E 1 q
2 (spherically symmetric)
0
Superposition
principle for electric fields
Electric field due
to
group
of
point charges is the
vector sum of the electric fields
produced
by
each charge individually
at
the given point.
➔ ➔
➔ ➔
E = E, + Ea + ...... +
E,
1 N
o
i=1
[1°-
151 (r
Electric
dipole
A pair of equal
and
opposite charges+ q and -
separated by some distance
2a
Electric dipole
moment
= Either charge x a vector drawn from
-q
to+
q
Property of a
medium
which determines the = q x 2
electric force between charges situated
in
that
medium,
Relative
permittivity
Direction of dipole moment is from
-q
to+
q
SI
unit
of dipole moment =
Cm
Ratio
of
the force between
two
charges placed
in
free
space to the force between the
same
two
charges placed the
same
distance
apart
in
a 1
medium.
Electric field
at
an
axial
point
of
a
dipole
At
distance r
>>a
,
E 1 2p
3(Direction
along )
0
vac
0
med
Principle
of
superposition
of
forces
The
net
force
on
a given charge is the vector
of
the
forces exerted
on
it
due
to all other charges.
or
F = Total force
on
charge q
due
to
many
point charges q'
11
N
47&g
all point
charges
r
q r
Continuous
charge
distribution
For
q
>>e
we
can
ignore
the
quantum
nature
of
charge
and
assume
that
the charge is distributed
in
a
continuous
manner.
Volume
charge density,
p=
Surface
charge
density,
a=
anear
charge
density,
d1
Cm
dV
d
Cm
dS
Electric field
at
an
equatorial
point
of
a
dipole
At
distance r
>>a,
1 p
F
g
■
~
4
e.
,a
(Direction antiparallel )
o r
Torque
on
a
dipole
in
a
uniform
electric field
If 0
is
the angle between 7
and
E,
=
pE
sin 0
or
t=
7 x E
Electric lines
of
force
A curve along which a small positive charge
tends
to move
in
an
electric field
and
the tan-
gent
to which
at
point
gives
the
direction of
electric field
at
that point.
Properties
of
electric
lines
of
force
1. Continuous curves
without
any
breaks.
2.
They
start
from +
ve
charges
and
end
on
negative charges.
3.
No
two lines
of
force can intersect each other.
4.
They
do
not
form closed loops.
5. Normal to the surface of a conductor.
6.
Their relative closeness measures
strength
of
electric
field.
Electric flux (Vector : SI
unit
NmC
~
)
Total
number
of electric lines of force passing
normally through a given area. If 0 is the angle
between E
and
normal to area element
AS,
then
A◊
=E
.A S
Gaussian
surface
Any
hypothetical surface enclosing a charge.
Gauss's
theorem
Total electric flux through a closed surface S is
equal to 1 /
e,
times the charge q enclosed
by
the
surface
S.
s E
0
Electric field
of
a line
charge
At
a perpendicular distance r .from a long
straight wire of a linear charge density
.,
E 1
0 r
Electric field
of
an
infinite
plane
sheet
of
charge
= surface charge density.
E
0
For
~
>0, the field is directed away from the sheet.
For
cr
< 0, the field is directed
towards
the sheet
Electric field
of
two
positively
charged
plates
For 0 >02 >0,
1
E = ±
~
(o,
+
o2)
2 € [Outside the plates]
0
E 1
2 € [Inside the plates]
0
Electric field
of
two
equally
and
oppositely
charged
parallel
plates
E E
0
[Outside the plates]
[Inside the plates]
Electric field
of
a
thin
spherical
shell
E 1 q
4m
E
E 0
E 1
0
0 R
[Outside points, r >R]
[Inside points, r <
R]
[At the surface, r =
R]
Electric field of a uniformly charged solid sphere
E
E
E
where q
~
3
1 q
4m E 2 [Outside points, r >R]
0 r
1
qr
4m € 0 R [Inside points, r
<R]
1
0 R [At the surface, r = R]
(1)
