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ELECTROSTATICS - I
– Electrostatic Force
1
...
Properties of Electric Charges
3
...
Coulomb’s Law in Vector Form
5
...
Relative Permittivity or Dielectric Constant
7
...
++
+
++
+
+
++
+
++
- -
Glass
Silk
+
++ +
+
++ +
++
...
So, when
glass and silk are rubbed together, the comparatively loosely bound electrons
from glass get transferred to silk
...
Electrons in fur are loosely bound in it than the electrons in ebonite
...
As a result, ebonite becomes negatively charged and fur becomes positively
charged
...
i
...
If the electrons are transferred from a body, then the deficiency of
electrons makes the body positive
...
If the two bodies from the following list are rubbed, then the body appearing
early in the list is positively charges whereas the latter is negatively charged
...
Column I (+ve Charge)
Column II (-ve Charge)
Glass
Silk
Wool, Flannel
Amber, Ebonite, Rubber, Plastic
Ebonite
Polythene
Dry hair
Comb
Properties of Charges:
1
...
2
...
3
...
4
...
eg
...
Charge is quantized
...
e
...
It can be expressed in integral multiples fundamental electronic charge
(e = 1
...
Charge is conserved
...
e
...
eg
...
The net
charge on the glass-silk system remains zero before and after rubbing
...
Note: Recently, the existence of quarks of charge ⅓ e and ⅔ e has been
postulated
...
However, the law of quantization will hold good
...
Strictly speaking, Coulomb’s law applies to stationary point charges
...
where ε0 is the permittivity of free space
In medium, k =
1
where ε is the absolute electric permittivity of
the dielectric medium
4πε
The dielectric constant or relative permittivity or specific inductive capacity or
dielectric coefficient is given by
ε
K = εr =
ε0
In vacuum, F =
In medium, F =
1
q1 q2
4πε0
r2
q1 q2
1
4πε0εr
r2
ε0 = 8
...
9875 x
109
N
m2
C-2
or
1
4πε0
= 9 x 109 N m2 C-2
Coulomb’s Law in Vector Form:
+ q1
In vacuum, for q1 q2 > 0,
F12 =
F21 =
1
q1 q2
4πε0
r2
1
q1 q2
4πε0
r2
+ q2
r12
r
F12
r21
F21
q1q2 > 0
r12
- q1
- q2
r12
r
F12
F21
q1q2 > 0
In vacuum, for q1 q2 < 0,
F12 =
1
q1 q2
4πε0
r2
r12 & F =
21
1
q1 q2
4πε0
r2
+ q1
r21
r12
F12
F21
r
F12 = - F21
(in all the cases)
- q2
q1q2 < 0
1
F12 =
4πε0
q1 q2
r3
r12
&
F21 =
1
q1 q2
4πε0
r3
r21
Note: The cube term of the distance is simply because of vector form
...
Units of Charge:
In SI system, the unit of charge is coulomb (C)
...
In cgs electrostatic system, the unit of charge is ‘statcoulomb’ or ‘esu of charge’
...
For vacuum, K = 1
...
In cgs electromagnetic system, the unit of charge is ‘abcoulomb’ or ‘emu of
charge’
...
ε
K = εr =
ε0
The dielectric constant or relative permittivity or specific inductive capacity or
dielectric coefficient can also be defined as the ratio of the electrostatic force
between two charges separated by a certain distance in vacuum to the
electrostatic force between the same two charges separated by the same
distance in that medium
...
Continuous Charge Distribution:
Any charge which covers a space with dimensions much less than its distance
away from an observation point can be considered a point charge
...
It is useful to consider the density of a charge distribution as we do for density
of solid, liquid, gas, etc
...
Linear charge density is the charge per unit length
...
dq
q
λ=
or
l
Total charge on line l,
λ=
dl
q = ∫ λ dl
l
dq
++++++++++++
dl
(ii) Surface Charge Density ( σ ):
If the charge is distributed over a surface area, then the distribution is called
‘surface charge distribution’
...
Its SI unit is C / m2
...
Volume charge density is the charge per unit volume
...
ρ=
dq
q
ז
Total charge on volume ז,
or
ρ=
dז
q = ∫ ρ dז
ז
dq
dז
ELECTROSTATICS - II : Electric Field
1
...
Electric Field Intensity or Electric Field Strength
3
...
Superposition Principle
5
...
Properties of Electric Lines of Force
7
...
Electric Field Intensity due to an Electric Dipole
9
...
Work Done on an Electric Dipole
Electric Field:
Electric field is a region of space around a charge or a system of charges
within which other charged particles experience electrostatic forces
...
Electric Field Strength or Electric Field Intensity or Electric Field:
Electric field strength at a point in an electric field is the electrostatic force per
unit positive charge acting on a vanishingly small positive test charge placed
at that point
...
Note:
1
...
2
...
3
...
4
...
Electric Field due to a Point Charge:
Y
Force exerted on q0 by q is
F=
or
F=
1
q q0
4πε0
r2
1
q q0
4πε0
r3
Electric field strength is
E (r) =
or
E (r) =
E=
1
F
r
+ q0
r
r
P (x,y,z)
+q
X
O
F
q0
q
4πε0
r3
1
q
4πε0
r2
Z
r
E
r
The electric field due to a point charge has
spherical symmetry
...
If q < 0, then the field is radially inwards
...
F1 = F12 + F13 + F14 + F15
Fa (ra) =
1
4πε0
N
∑ qa qb
b=1
b≠a
ra - rb
- q5
+ q1
F12
F13
- q3
+ q4
F12
F1
│ ra - rb │3
In the present example, a = 1 and b = 2 to 5
...
+ q2
F15
F15
F13
F14
Note:
The interactions must be on the charge which is to be studied due to other
charges
...
For eg
...
The interactions between the other charges (among themselves) must be
ignored
...
e
...
Superposition principle holds good for electric field also
...
Electric lines of force do not physically exist but they represent real situations
...
Electric Lines of Force due to a Point Charge:
a) Representation
of electric field
in terms of
field vectors:
The size of the
arrow
represents the
strength of
electric field
...
Electric Lines of Force due to a
3
...
N
+q
-q
Electric lines of force contract
lengthwise to represent attraction
between two unlike charges
...
4
...
The electric lines of force are imaginary lines
...
A unit positive charge placed in the electric field tends to follow a path
along the field line if it is free to do so
...
The electric lines of force emanate from a positive charge and terminate on
a negative charge
...
4
...
5
...
If they do, then at the point of
intersection, there will be two tangents
...
Further, electric field being a vector quantity,
there can be only one resultant field at the
given point, represented by one tangent at the
given point for the given line of force
...
Electric lines of force are closer
(crowded) where the electric field
is stronger and the lines spread
out where the electric field is
weaker
...
Electric lines of force are
perpendicular to the surface of a
positively or negatively charged
body
...
Electric lines of force contract lengthwise to represent attraction between
two unlike charges
...
Electric lines of force exert lateral (sideways) pressure to represent
repulsion between two like charges
...
The number of lines per unit cross – sectional area perpendicular to the
field lines (i
...
density of lines of force) is directly proportional to the
magnitude of the intensity of electric field in that region
...
Electric lines of force do not pass through a conductor
...
+
+
+
+
+
+
+
E
E
-
Solid or hollow +
+
conductor
+
No Field
+
-
(Electrostatic Shielding)
12
...
Electric Dipole:
Electric dipole is a pair of equal and opposite charges separated by a very
small distance
...
Electric dipole moment is a vector quantity used to measure the strength of an
electric dipole
...
The direction is from negative to positive charge
...
Note:
An ideal dipole is the dipole in which the charge becomes larger and larger
and the separation becomes smaller and smaller
...
l
l
x
│EP │ = │EB│ - │EA│
EA =
EB =
│EP │ =
│EP │ =
│EP │ =
1
q
4πε0
(x + l)2
1
q
4πε0
(x - l)2
1
4πε0
i
EP =
i
q
[ (x - l)
2
q
-
1
2 (q
...
ii) At a point on the equatorial line:
Resultant electric field intensity
at the point Q is
EQ = EA + EB
EB
EA =
EB =
1
q
1
Q
θ
i
EA cos θ θ
θ
θ
O
-q
4πε0 ( x2 + l2 )
The vectors EA cos θ and EB cos θ
are acting along the same direction
and hence add up
...
Q
EQ
EA
A
EB sin θ
EB cos θ θ
y
4πε0 ( x2 + l2 )
q
θ
EQ
The vectors EA and EB are
acting at an angle 2θ
...
2l
4πε0 ( x2 + l2 )3/2
1
p
4πε0 ( x2 + l2 )3/2
l
( x2 + l2 )½
EQ =
1
p
4πε0 ( x2 + l2 )3/2
(- i )
If l << y, then
EQ ≈
p
4πε0 y3
The direction of electric field intensity at a point on the equatorial line due to a
dipole is parallel and opposite to the direction of the dipole moment
...
i
...
If l << x and l << y, then EP = 2 EQ
Torque on an Electric Dipole in a Uniform Electric Field:
The forces of magnitude pE act
opposite to each other and hence net
force acting on the dipole due to
external uniform electric field is zero
...
+q
qE
2l
qE
θ
p
-q
E
However the forces are along different
lines of action and constitute a couple
...
Torque = Electric Force x
p
θ
distance
t = q E (2l sin θ)
E
t
= p E sin θ
t = pxE
Direction of Torque is perpendicular
and into the plane containing p and E
...
Case i: If θ = 0°, then t = 0
...
Case iii: If θ = 180°, then t = 0
...
dW = tdθ
qE
dθ + q q E
= p E sin θ dθ
2l
θ1 θ2
-q
θ2
W = ∫ p E sin θ dθ
θ1
qE
qE
E
W = p E (cosθ1 - cos θ2)
If Potential Energy is arbitrarily taken zero when the dipole is at 90°,
then P
...
Case i: If θ = 0°, then U = - pE
(Stable Equilibrium)
Case ii: If θ = 90°, then U = 0
Case iii: If θ = 180°, then U = pE (Unstable Equilibrium)
ELECTROSTATICS - III
- Electrostatic Potential and Gauss’s Theorem
1
...
Electric Potential and Potential Difference
3
...
Electric Potential due to a Group of Charges
5
...
Equipotential Surfaces and their Properties
7
...
Area Vector, Solid Angle, Electric Flux
9
...
Coulomb’s Law from Gauss’s Theorem
11
...
B
Y
WAB = dW = - E
...
+q0
rA
r
The force F = +q0E acts on the test charge
due to the source charge +q
...
To prevent this
acceleration, equal and opposite force –q0E
has to be applied on the test charge
...
dl =
A
qq0
4πε0
1
1
[r
B
-
rA
]
B
WAB = dW = - E
...
The equation shows that the work done in moving a test charge q0 from
point A to another point B along any path AB in an electric field due to +q
charge depends only on the positions of these points and is independent of
the actual path followed between A and B
...
That is, the line integral of electric field is path independent
...
Therefore, electric field is ‘conservative field’
...
Line integral of electric field over a closed path is zero
...
B
E
...
However, line integral of the field due to a moving charge is not independent
of the path because the field varies with time
...
It is a physical quantity that determines the degree of electrification of a body
...
B
E
...
Electric potential at a point is one volt if one joule of work is done in moving
one coulomb charge from infinity to that point in the electric field
...
B
E
...
Electric potential and potential difference are scalar quantities
...
Electric potential at infinity is zero
...
Electric potential near an isolated positive charge (q > 0) is positive and that
near an isolated negative charge (q < 0) is negative
...
cgs unit of electric potential is stat volt
...
E
dx +q0
B
+q
Q
q0 E
∞
P
r
The force F = +q0E is
radially outward and tends
to accelerate the test charge
...
Work done to move q0 from P to Q through ‘dx’ against q0E is
dW = F
...
dx
q q0
dW = -
dx
4πε0 x2
or
dW = q0E dx cos 180° = - q 0E dx
q
E=
4πε0 x2
Total work done to move q0 from A to B (from ∞ to r ) is
B
W∞B =
r
q q0
dW = ∞
r
∞
4πε0 x2
dx
=-
q q0
1
4πε0 x2
x2
∞
dx
q
W∞B
=
q0
4πε0 r
q
V =
4πε0 r
Electric Potential due to a Group of Point Charges:
The net electrostatic potential at a point in the
electric field due to a group of charges is the
algebraic sum of their individual potentials at that
point
...
Electric potential at a point due to a charge is not affected by the presence
of other charges
...
Potential, V α 1 / r whereas Coulomb’s force F α 1 / r2
...
Potential is a scalar whereas Force is a vector
...
Although V is called the potential at a point, it is actually equal to the
potential difference between the points r and ∞
...
2l
4πε0
(x2 – l2)
1
p
4πε0 (x2 – l2)
l
x
q-
1
+q
p
4πε0 (x + l)
VP = VP
VP =
-q
1
=
A
-
1
(x + l)
]
+1 C
P
ii) At a point on the equatorial line:
VQ
VQ
q+
q-
=
1
q
4πε0
BQ
1
-q
=
4πε0
Q
y
AQ
A
VQ = VP
VQ =
q+
+ VP
q
4πε0
VQ = 0
[
θ
θ
-q
q-
B
+q
O
p
1
-
BQ
1
AQ
]
l
l
BQ = AQ
The net electrostatic potential at a point in the electric field due to an electric
dipole at any point on the equatorial line is zero
...
i) For a uniform electric field:
E
V1
V2
V3
Plane Equipotential Surfaces
E
+
Spherical Equipotential Surfaces
ii) For an isolated charge:
Properties of Equipotential Surfaces:
1
...
WAB
VB - VA = ∆V =
q0
If A and B are two points on the equipotential surface, then VB = VA
...
The electric field is always perpendicular to the element dl of the
equipotential surface
...
dl = 0
i
...
E dl cos θ = 0
A
As E ≠ 0 and dl ≠ 0,
cos θ = 0
or
θ = 90°
3
...
Electric field is defined as the negative potential gradient
...
e
...
e
...
4
...
If two equipotential surfaces intersect, then at the points of intersection,
there will be two values of the electric potential which is not possible
...
The negative sign of potential gradient shows that the rate of change of
potential with distance is always against the electric field intensity
...
W=qV
i) Electrostatic Potential Energy
of a Two Charges System:
U =
Y
A (q1)
q1q2
1
r1
│ r2 - r1 │
4πε0
r2 - r1
B (q2)
r2
or
U=
O
1
q1q2
4πε0
r12
Z
X
ii) Electrostatic Potential Energy
of a Three Charges System:
U=
q1q2
1
│ r2 - r1 │
4πε0
+
+
or
U=
1
4πε0
[
q1q2
r12
+
Y
A (q1)
q1q3
1
r2 - r1
r3
r2
q2q3
1
4πε0
│ r3 - r2 │
q1q3
q2q3
r31
r3 - r1
r1
│ r3 - r1 │
4πε0
C (q3)
+
r32
O
Z
]
iii) Electrostatic Potential Energy of an n - Charges System:
U=
1
2
[
1
4πε0
n
n
∑ ∑
i=1
qi qj
j=1 │ rj
i≠j
- ri │
]
r3 - r2
B (q2)
X
Area Vector:
n
Small area of a surface can be represented by a vector
...
dS
Electric flux dΦ through a small area
element dS due to an electric field E at an
angle θ with dS is
dΦ = E
...
dS = E S cos θ = E
...
But it is a
property of vector field
...
θ
dS
Total electric flux Φ over the whole
surface S due to an electric field E is
Φ=
dS
θ
dS
E
Special Cases:
1
...
2
...
3
...
Solid Angle:
Solid angle is the three-dimensional equivalent of an ordinary twodimensional plane angle
...
r
Solid angle subtended by area element dS at the
centre O of a sphere of radius r is
θ
dS cos θ
dΩ =
r
dS cos θ
Ω = dΩ =
S
dS
r2
S
r2
= 4π steradian
dΩ
n
Gauss’s Theorem:
The surface integral of the electric field intensity over any closed hypothetical
surface (called Gaussian surface) in free space is equal to 1 / ε0 times the net
charge enclosed within the surface
...
dS =
ε0
S
∑ qi
i=1
Proof of Gauss’s Theorem for Spherically Symmetric Surfaces:
dΦ = E
...
dS n
E
r
r
...
n = 1 x 1 cos 0°= 1
dΦ =
ΦE =
1
q dS
4πε0
r2
1
q
4πε0
r2
dΦ =
S
dS =
S
dS
1
q
4πε0
r2
4π r2 =
q
ε0
Proof of Gauss’s Theorem for a Closed Surface of any Shape:
dΦ = E
...
dS n
r
θ
r
...
n = 1 x 1 cos θ
= cos θ
dΩ
+q •
dΦ =
ΦE =
4πε0
dΦ =
S
dS cos θ
q
r2
q
dΩ =
4πε0
S
q
4πε0
q
4π
=
ε0
n
Deduction of Coulomb’s Law from Gauss’s Theorem:
From Gauss’s law,
q
ΦE =
E
...
Applications of Gauss’s Theorem:
1
...
dS =
l
E
q
ΦE =
E
ε0
S
E
...
dS +
S
A
E
...
dS +
B
E
...
C
C
q
ε0
λl
= ε
0
(where λ is the liner charge density)
λl
ε0
Ex2πrl=
or
1
E=
2 πε0
λ
r
or
1
E=
4 πε0
2λ
r
In vector form,
1
E (r) =
4 πε0
2λ
r
r
The direction of the electric field intensity is radially outward from the positive
line charge
...
Note:
The electric field intensity is independent of the size of the Gaussian surface
constructed
...
i
...
the
Gaussian surface should contain the point of consideration
...
Electric Field Intensity due to an Infinitely Long, Thin Plane Sheet of
Charge:
σ
dS
l
r
dS
E
E
C
E
A
B
dS
From Gauss’s law,
q
ΦE =
E
...
S
E
...
dS +
S
A
E
...
dS +
B
C
E dS cos 0°+
A
E
...
For negative charge distribution, it will
be towards the plane
...
It neither depends on the distance of point of consideration nor
the radius of the cylindrical surface
...
So, the charge enclosed within the Gaussian surface will be
twice as before
...
E=
σ
ε0
3
...
Electric Field Intensity due to a Uniformed Charged This Spherical
Shell:
E
i) At a point P outside the shell:
dS
r
•P
From Gauss’s law,
q
ΦE =
E
...
ii) At a point A on the surface of the shell:
From Gauss’s law,
E
q
ΦE =
E
...
iii) At a point B inside the shell:
From Gauss’s law,
dS
q
ΦE =
E
...
O
R
r
ELECTROSTATICS - IV
- Capacitance and Van de Graaff Generator
1
...
Electrical Capacitance
3
...
Capacitance of a Parallel Plate Capacitor
5
...
Energy Stored in a Capacitor and Energy Density
7
...
Loss of Energy on Sharing Charges Between Two Capacitors
9
...
Polarization of a Dielectric
11
...
Parallel Plate Capacitor with a Dielectric Slab
13
...
Net electric field intensity in the interior of a
conductor is zero
...
At an
equilibrium, the electric field due to the
polarisation becomes equal to the applied
field
...
E0
EP
Enet = 0
2
...
Suppose the electric field is acting at an
angle other than 90°, then there will be a
component E cos θ acting along the tangent
at that point to the surface which will tend to
accelerate the charge on the surface leading
to ‘surface current’
...
So, θ = 90°and
cos 90°= 0
...
Net charge in the interior of a conductor is zero
...
The total
charge of the system is zero
...
dS = ε
0
S
Since E = 0 in the interior of the conductor,
therefore q = 0
...
Charge always resides on the surface of a
conductor
...
Construct a Gaussian surface just
inside the conductor
...
5
...
dV = - E
...
i
...
V = constant
q
q
q=0
6
...
q
σ=
S
σmin
Every conductor is an equipotential volume
(three- dimensional) rather than just an
equipotential surface (two- dimensional)
...
q
q α V or q = C V
or
C=
V
If V = 1 volt, then C = q
Capacitance of a conductor is defined as the charge required to raise its
potential through one unit
...
Symbol of capacitance:
Capacitance is said to be 1 farad when 1 coulomb of charge raises the
potential of conductor by 1 volt
...
Capacitance of an Isolated Spherical Conductor:
Let a charge q be given to the sphere which
is assumed to be concentrated at the centre
...
Capacitance of a spherical conductor is directly proportional to its radius
...
The above equation is true for conducting spheres, hollow or solid
...
IF the sphere is in a medium, then C = 4πε0εr r
...
Capacitance of the earth is 711 µF
...
Step 2: When a neutral plate B is brought near A,
charges are induced on B such that the side near A is
negative and the other side is positive
...
Step 3: When the farther side of B is earthed the
positive charges on B get neutralised and B is left only
with negative charges
...
To increase the potential to the same value as was in
step 2, an additional amount of charges can be given to
plate A
...
The system so formed is called a ‘capacitor’
...
σ
d
V=Ed=
ε0
σ
σ
E
A
A
qd
or
V=
A ε0
q
But
C=
C=
V
A ε0
d
d
If the space between the plates is filled with dielectric medium of relative
permittivity εr, then
A ε0 εr
C=
d
Capacitance of a parallel plate capacitor is
(i) directly proportional to the area of the plates and
(ii) inversely proportional to the distance of separation between them
...
e
...
Note: The effective capacitance in series combination is less than the least of
all the individual capacitances
...
e
...
Note: The effective capacitance in parallel combination is larger than the
largest of all the individual capacitances
...
The moment charging starts, there is a potential
difference between the plates
...
This work is stored as
electrostatic potential energy in the capacitor
...
Energy density is generalised as energy per unit volume of the field
...
+
1
U=
2
q2
[
1
C1
1
Cn
+
1
C2
+
1
C3
+ ………
...
+ Un
The total energy stored in the system is the sum of energy stored in the
individual capacitors
...
+ Cn
1
C
U=
1
V2
U=
2
2
V2 ( C1 + C2 + C3 + ………
...
+ Un
The total energy stored in the system is the sum of energy stored in the
individual capacitors
...
Total charge after sharing = Total charge before sharing
(C1 + C2) V = C1 V1 + C2 V2
V=
C1 V1 + C2 V2
C1 + C2
The total energy before sharing is
1
Ui =
2
C1 V1
2
1
+
2
C2 V22
The total energy after sharing is
1
Uf =
2
Ui– Uf =
(C1 + C2) V2
C1 C2 (V1 – V2)2
Ui – Uf > 0
2 (C1 + C2)
or Ui > Uf
Therefore, there is some loss of energy when two charged capacitors are
connected together
...
Polar Molecules:
A molecule in which the centre of positive charges does
not coincide with the centre of negative charges is called
a polar molecule
...
p
H
Eg
...
H
Effect of Electric Field on Polar Molecules:
E=0
p=0
In the absence of external electric
field, the permanent dipoles of the
molecules orient in random
directions and hence the net dipole
moment is zero
...
Complete
allignment is not possible due to
thermal agitation
...
Non-polar molecule has symmetrical shape
...
N2 , C H4, O2, C6 H6, etc
...
When electric field is applied, the positive
charges are pushed in the direction of electric
field and the electrons are pulled in the
direction opposite to the electric field
...
Dielectrics:
Generally, a non-conducting medium or insulator is called a ‘dielectric’
...
Eg
...
Polarization of Dielectrics:
When a non-polar dielectric slab is
subjected to an electric field, dipoles
are induced due to separation of
effective positive and negative centres
...
The net field is EN = E0 – Ep
i
...
the field is reduced when a
dielectric slab is introduced
...
It
is defined as the dipole moment of the unit volume of the polarized dielectric
...
Dielectric Strength:
Dielectric
Dielectric strength (kV /
mm)
Dielectric strength is the maximum
value of the electric field intensity
that can be applied to the dielectric
without its electric break down
...
Pyrex
14
Its practical unit is kV mm-1
...
8 – 1
4–8
21
160 – 200
Capacitance of Parallel Plate Capacitor with Dielectric Slab:
V = E0 (d – t) + EN t
E0
K=
or
EN
EN =
But
and
K
t
[ (d – t) +
E0 =
σ
ε0
K
E0
V = E0 (d – t) +
V = E0
E0
K
Ep
EN = E0 - Ep
t
d
t
]
qA
=
E0
or
A ε0
C=
t
[
ε0
d 1–
(1 -
d
q
C=
t
)
]
K
C0
V
or
A ε0
C=
[ (d – t) +
t
K
C=
[1 –
]
t
d
(1 -
t
)
]
K
C > C0
...
e
...
If the dielectric slab occupies the whole space between the plates, i
...
t = d,
then
C = K C0
Dielectric Constant
C
K=
C0
WITH DIELECTRIC SLAB
Physcial Quantity
With Battery
disconnected
With Battery
connected
Charge
Remains the same
Increases (K C0 V0)
Capacitance
Increases (K C0)
Increases (K C0)
Electric Field
Decreases
EN = E0 – Ep
Remains the same
Potential Difference Decreases
Remains the same
Energy stored
Increases (K U0)
Remains the same
Van de Graaff Generator:
S
P2
C2
S – Large Copper sphere
D
C1, C2 – Combs with sharp points
P1, P2 – Pulleys to run belt
HVR – High Voltage Rectifier
M – Motor
T
IS – Insulating Stand
I S
C1
D – Gas Discharge Tube
T - Target
HVR
P1
M
Principle:
Consider two charged conducting spherical shells such that one is
smaller and the other is larger
...
i
...
The charge resides on the outer surface of the outer shell and
the potential of the outer shell increases considerably
...
Therefore air surrounding these conductors get ionized and the like
charges are repelled by the charged pointed conductors causing
discharging action known as Corona Discharge or Action of Points
...
Opposite charges are induced on the teeth of collecting comb (conductor)
and again opposite charges are induced on the outer surface of the
collecting sphere (Dome)
...
A belt made of insulating fabric (silk, rubber, etc
...
Comb (C1) near the lower pulley is connected to High Voltage Rectifier
(HVR) whose other end is earthed
...
A tube (T) with the charged particles to be accelerated at its top and
the target at the bottom is placed as shown in the figure
...
To avoid the leakage of charges from the sphere, the generator is
enclosed in the steel tank filled with air or nitrogen at very high pressure
(15 atmospheres)
...
Due to action of points, electric wind is
caused and the positive charges are sprayed on to the belt (silk or
rubber)
...
The comb (C2) is induced with the negative charges which are
carried by conduction to inner surface of the collecting sphere
(dome) S through a metallic wire which in turn induces positive
charges on the outer surface of the dome
...
Therefore the belt does not carry
any charge back while descending
...
)
Contd
...
When the charge on the sphere is very high, the
leakage of charges due to ionization of surrounding air also
increases
...
Now, if the positively charged particles which are to be
accelerated are kept at the top of the tube T, they get accelerated
due to difference in potential (the lower end of the tube is
connected to the earth and hence at the lower potential) and are
made to hit the target for causing nuclear reactions, etc
...
The beam of accelerated charged particles are used to
trigger nuclear reactions
...
In medicine, such beams are used to treat cancer
...