Electrostatic and magnetostatics

Unit-2
Electrostatics
&
Magnetostatics

Coulomb’s Law – Gives the electric force
between two point charges.
2
2
1
r
q
q
k
F 
k = Coulomb’s Constant = 9.0x109 Nm2/C2
q1 = charge on mass 1
q2 = charge on mass 2
r = the distance between the two charges
The electric force is much stronger than the
gravitational force.
Inverse Square
Law

Example
•Two 40 gram masses each with a charge of 3μC are placed 50cm
apart. Compare the gravitational force between the two masses
to the electric force between the two masses. (Ignore the force
of the earth on the two masses)
3μC
40g
50c
3μC
40g
2
2
1
r
m
m
G
Fg 
2
11
)
5
.
0
(
)
04
)(.
04
(.
10
67
.
6 

 N
13
10
27
.
4 


2
2
1
r
q
q
k
FE  2
6
6
9
)
5
.
0
(
)
10
3
)(
10
3
(
10
0
.
9





 N
324
.
0

The electric force is much greater than the
gravitational force

Cont..Relation between E and V

Cont..
●Maxwell Equation From Gauss Law
We know that
●Integrating both side. Further using
Divergence law in left hand side and total
charge in integral form
●Now comparing both side, we can Maxwell
first equation as

Cont..
●Poission and Laplace Equation From Gauss Law

21-10-2015 FCI 30
Capacitors are commonly used in a
variety of electric circuits. For
instance, they are used to tune the
frequency of radio receivers, as
filters in power supplies, to
eliminate sparking in automobile
ignition systems, and as energy-
storing devices in electronic
flash units.
A capacitor consists of two conductors separated by an
insulator. The capacitance of a given capacitor depends on its
geometry and on the material—called a dielectric— that
separates the conductors.
Capacitance and Capacitor

Cont..
The capacitance C of a capacitor is defined as the ratio of
the magnitude of the charge on either conductor to the
magnitude of the potential difference between the
conductors:
The SI unit of capacitance is the farad (F),
Note that by definition capacitance is always a positive
quantity. Furthermore, the charge Q and the potential
difference ΔV are positive quantities. Because the
potential difference increases linearly with the stored
charge, the ratio Q / Δ V is constant for a given capacitor.
21-10-2015 FCI 31

Cont..
The charge, Q, on a capacitor is directly proportional to the potential difference, V,
across the capacitor. That is,
Q α V
Introducing a constant, C, known as the capacitance of the capacitor, we have
Q = CV
Capacitance of a capacitor is defined as the ratio of charge on one of the
capacitor plates to the potential difference between the plates.
Charge Q is measured in coulombs, C.
Potential difference, V, is measured in volts, V.
Capacitance, C, is measured in farads, F.
1 farad is 1 coulomb per volt: 1 F = 1 C V-1
1 farad is a very large unit. It is much more common to use the
following:
mF = 10-3 F , μF = 10-6 F , nF = 10-9 F , pF = 10-12 F

Cont.. - Energy Stored in an Electric Field
Suppose that, at a given instant, a charge q′ has
been transferred from one plate of a capacitor to
the other. The potential difference V′ between
the plates at that instant will be q′/C. If an extra
increment of charge dq′ is then transferred, the
increment of work required will be,
21-10-2015 FCI 33
The work required to bring the total capacitor charge up to a final value q is
This work is stored as potential energy U in the capacitor, so that
or
The potential energy of a charged capacitor may be viewed
as being stored in the electric field between its plates.

Is the B-Field From a Power Line Dangerous?
A power line
carries a current of
500 A.
What is the
magnetic field in a
house located
100 m away from
the power line?
R
i
B
p
m
2
0
=
=
(4p ´10-7
T × m/A)(500A)
2p(100m)
= 1 T
Recall that the earth’s
magnetic field is ~10–4T = 100
T
Probably not dangerous!

Cont..
●Maxwell Second Equation
The Gauss’s law for magnetism states that net
flux of the magnetic field through a closed
surface is zero because monopoles of a
magnet do not exist. i.e.

Cont..
●Maxwell Equation From Ampere's law
We know that Ampere's law in integral fom as
●Using Stokes Theorem
●Total current enclosed is defines as
●From above two equations
●Comparing both side, we get Maxwell Fourth Equ

Cont..
●Maxwell Equation From Faraday's law
We know that Faraday's law is
●Electric Potential or
●Further
●From Stokes Theorem
●Using above equations
●This is Maxwell 3rd Equation

Magnetic Scalar and Vector Potential

Electrostatic and magnetostatics

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