The document discusses magnetostatics and provides definitions and explanations of key concepts including magnetic field, magnetic flux, Biot-Savart law, Ampere's law, solenoids, ballistic galvanometers, and damping conditions. Specific topics covered include the magnetic field produced by steady currents, magnetic field lines, curl and divergence of magnetic fields, theory and operation of ballistic galvanometers, and current and charge sensitivity of galvanometers. Examples and derivations of equations for magnetic fields and forces on conductors in fields are also provided.

1. M a g n e t o s t a t i c s
Presentation by
Parasa srivarsha
Lecturer in physics
SARDAR PATEL COLLEGE

2. Magentostatics
Electomagnetics
Magentic field produced by steady
current

3. Topics:
Magnetic field
Magnetic flux
Biot savarts law
Amperes law and it's applications
Ballastic galvanometer and its
applications

4. Magnetic field
 The region around a magnet that gets
influenced by the strength of magnet is
known as magnetic field B
 B=Force/pole strength of the pole place at
distance (d)
 Magnetic field B SI unit is Tesla
 Magnetic flux is defined as the total
number of lines of induction cutting
through a surface .

5.  Magnetic lines of force are define as a path in a
magentic field where an isolated unit north pole can
move freely
 Magnetic induction field strength at a point is defined as
a force experienced by a unit north pole at a distance d
in a magentic field .
 Field intensity is also know aa magnetizng force it is
defined as the magneto motive force per unit length of
amper turn per meter
H =NI/Lamper turn per meter .
where N =no .of turns of coil , I =current in amperes
L = length of magnetic path involves

6. Properties of magentic field:
 Magnetic fields can be pictorially
represented by magnetic field
lines, the properties of which are
as follows:
 The field is tangent to the
magnetic field line.
 Field strength is proportional to
the line density.
 Field lines cannot cross.
 Field lines are continuous loops.

7. Biot-savarts law
 Statement: Biot savarts law states that magnetic field intensity dH at
a point P due to a current element Idl Is
 dH Directly proportional to Current element Idl
 dH directly proportional to Sine of the angle between Idl and line
joining the point p to the element .
 dH is inversely proportional to square of distance between the point
and the current element r.

8. B due to current carring conductor
Consider an infinitely long
conductor AB through which
current I flows. Let P be any
point at a distance a from the
centre of conductor.
Consider dl be the small
current carrying element at
point c at a distance r from
point p. α be the angle
between r and dl. l be the
distance between centre of
the coil and elementary
length dl.
From biot-savart law,

11. Derivation of ampere’s law
 Figure

12. Amperes law
 The magnetic field in space around an electric current is proportional to the electric
current which serves as its source, just as the electric field in space is proportional to
the charge which serves as its source. Ampere's Law states that for any closed loop
path, the sum of the length elements times the magnetic field in the direction of the
length element is equal to the permeability times the electric current enclosed in the
loop.

In the electric case, the relation of field to source is quantified in Gauss's Law which is
a very powerful tool for calculating electric fields

13.  Ampere's Law Applications

14. Solenoid
 long straight coil of wire can be used to
generate a nearly uniform magnetic
field similar to that of a bar magnet. Such
coils, called solenoids, have an enormous
number of practical applications. The field
can be greatly strengthened by the addition
of an iron core. Such cores are typical
in electromagnets.
 In the above expression for the magnetic
field B, n = N/L is the number of turns per
unit length, sometimes called the "turns
density". The magnetic field B is
proportional to the current I in the coil. The
expression is an idealization to an infinite
length solenoid, but provides a good
approximation to the field of a long
solenoid.

15. Magentic field in a circular loop
 Examining the direction of the magnetic field produced by a current-carrying segment
of wire shows that all parts of the loop contribute magnetic field in the same direction
inside the loop
 Electric current in a circular loop creates a magnetic field which is more concentrated in
the center of the loop than outside the loop. Stacking multiple loops concentrates the
field even more into what is called a solenoid.

16. Solenoid Field from Ampere's Law
 Taking a rectangular path about which to evaluate Ampere's Law such that the length of
the side parallel to the solenoid field is L gives a contribution BL inside the coil. The
field is essentially perpendicular to the sides of the path, giving negligible contribution.
If the end is taken so far from the coil that the field is negligible, then the length inside
the coil is the dominant contribution.

17. Magnetic Field at centre of loop

18. Magnetic field on axis of current loop

19. Force on a charged point in a magentic field
 The magnetic field B is defined from the Lorentz Force Law, and specifically from the
magnetic force on a moving charge
 implications of this expression include:
 1. The force is perpendicular to both the velocity v of the charge q and the magnetic
field B.
 2. The magnitude of the force is F = qvB sinθ where θ is the angle < 180 degrees
between the velocity and the magnetic field. This implies that the magnetic force on a
stationary charge or a charge moving parallel to the magnetic field is zero.
 3. The direction of the force is given by the right hand rule. The force relationship
above is in the form of a vector product.

20.  When the magnetic force relationship is applied to a current-carrying wire, the right-
hand rule may be used to determine the direction of force on the wire.
 From the force relationship above it can be deduced that the units of magnetic field are
Newton seconds /(Coulomb meter) or Newtons per Ampere meter. This unit is named
the Tesla. It is a large unit, and the smaller unit Gauss is used for small fields like the
Earth's magnetic field. A Tesla is 10,000 Gauss. The Earth's magnetic field at the
surface is on the order of half a Gauss.

21. Curl and divergence of magentic field
Line Integrals of Magnetic Fields
 Recall that while studying electric fields we established that the surface integral
through any closed surface in the field was equal to 4Π times the total charge
enclosed by the surface. We wish to develop a similar property for magnetic
fields. For magnetic fields, how ever, we do not use a closed surface, but a
closed loop. Consider a closed circular loop of radius R about a straight wire
carrying a current I, as shown below.


22.  A closed path around a straight wireWhat is the line integral around this closed
loop? We have chosen a path with constant radius, so the magnetic field at
every point on the path is the same: B = .
 addition, the total length of the path is simply the circumference of the
circle: L = 2Πr. Thus, because the field is constant on the path, the line integral
is simply

23.  This equation, called Ampere's Law, is quite convenient. We have generated an
equation for the line integral of the magnetic field, independent of the position
relative to the source. In fact, this equation is valid for any closed loop around the
wire, not just a circular one.
 @@Equation @@ can be generalized for any number of wires carrying any
number of currents in any direction. We won't go through the derivation, but will
simply state the general equation.

24.  Note that the path need not be circular or perpendicular to the wires. The figure
below shows a configuration of a closed path around a number of wires:
 The line integral around the circle in the figure is equal to (I1 + I2 - I3 - I4).
 Notice that the two wires pointing downwards are subtracted, since their field
points in the opposite direction from the curve.
 This equation, similar to the surface integral equation for electric fields, is
powerful and allows us to greatly simplify many physical situations.

25. The Curl of a Magnetic Field
1. From this equation, we can generate an expression for the curl of a
magnetic field. Stokes' Theorem states that:
2. We have established that
3. So, to remove the integral form this equation include concept density

26.  Thus the curl of a magnetic field at any point is equal to the current density at
that point. This is the simplest statement relating the magnetic field and moving
charges. It is mathematically equivalent to the line integral equation we
developed before, but is easier to work with in a theoretical sense.
 The Divergence of the Magnetic Field
 Recall that the divergence of the electric field was equal to the total charge
density at a given point. We have already examined qualitatively that there is no
such thing as magnetic charge. All magnetic fields are, in essence, created by
moving charges, not by static ones. Thus, because there are no magnetic
charges, there is no divergence in a magnetic field
 :
 This fact remains true for any point in any magnetic field. Our expressions for
divergence and curl of a magnetic field are sufficient to describe uniquely any
magnetic field from the current density in the field. The equations for divergence
and curl are extremely powerful; taken together with the equations for the
divergence and curl for the electric field, they are said to encompass
mathematically the entire study of electricity and magnetism.


27. Energy in terms of inductance
 When a electric current is flowing in an inductor, there is energy stored in
the magnetic field. Considering a pure inductor L, the
instantaneous power which must be supplied to initiate the current in the
inductor is
 the energy input to build to a final current i is given by the integral
 Using the example of a solenoid, an expression for the energy density can be
obtained.

28. Energy in magnetic field
 From analysis of the energy stored in an inductor
 the energy density (energy/volume) is
 so the energy density stored in the magnetic field is


29.  Definition: The galvanometer which is used for
estimating the quantity of charge flow through
it is called the ballistic galvanometer. The
working principle of the ballistic galvanometer
is very simple. It depends on the deflection of
the coil which is directly proportional to the
charge passes through it.

30. Ballistic galvanometer
 Definition: The galvanometer which is used for estimating the quantity of
charge flow through it is called the ballistic galvanometer.
 The working principle of the ballistic galvanometer is very simple. It depends
on the deflection of the coil which is directly proportional to the charge
passes through it. The galvanometer measures the majority of the charge
passes through it in spite of current.
 Construction of Ballistic Galvanometer
 The ballistic galvanometer consists coil of copper wire which is wound on the
non-conducting frame of the galvanometer. The phosphorous bronze suspends
the coil between the north and south poles of a magnet. For increasing
the magnetic flux the iron core places within the coil. The lower portion of
the coil connects with the spring. This spring provides the restoring torque to
the coil.

32.  When the charge passes through the galvanometer, their coil
starts moving and gets an impulse. The impulse of the coil is
proportional to the charges passes through it. The actual
reading of the galvanometer achieves by using the coil having
a high moment of inertia. The moment of inertia means the
body oppose the angular movement. If the coil has a high
moment of inertia, then their oscillations are large. Thus,
accurate reading is obtained.
Theory of Ballistic Galvanometer
 Consider the rectangular coil having N number of turns placed
in a uniform magnetic field. Let l be the length and b be
the breadth of the coil. The area of the coil is given as

33.  When the current passes through the coil, the torque acts on it. The
given expression determines the magnitude of the torque.
 Let the current flow through the coil for very short duration says dt
and it is expressed as
 If the current passing through the coil for t seconds, the expression
becomes
The q be the total charge passes through the coil. The moment of inertia
of the coil is given by l, and the angular velocity through ω. The
expression gives the angular momentum of the coil

34.  The angular momentum of the coil is equal to the force acting on the
coil. Thus from equation (4) and (5), we get
 The Kinetic Energy (K) deflects the coil through an angle θ, and this
deflection is restored through the spring.
The resorting torque of the coil is equal to their deflection. Thus,
 The periodic oscillation of the coil is given as

35. By multiplying the equation (7) from the above
equation we get
On substituting the value of equation (6) in the
equation (8) we get

36. The K is the constant of the ballistic galvanometer.

37. Current and charge sensitivity
 Current sensitivity (Figure of merit): The figure of merit or current
sensitivity of a moving coil galvanometer is the current required to
produce a deflection of 1 mm on a scale kept at a distance of 1 m
from the mirror. It is expressed in μA/mm.
 Charge sensitivity is the charge generated in the PZT for every 'g' of
input acceleration. The unit for charge sensitivity is pF/ g.

38. Damping condition of galvanometer
 The damping effect of Eddy Currents is used in some moving coil
galvanometers to make them dead-beat. The coil of such
galvanometres is wound on a light metal frame. When the coil and
the frame rotate in the field of the permanent magnet, the eddy
currents set up in the frame oppose the motion so that the coil
returns to zero quickly.
 The oscillations of moving coil ballistic Galvanometer are stopped
by short circuiting the coil, this being due to the induced current
in the coil itself.
 A similar damping device is used in some instruments such as the
balances, ammeters and voltmeters. A copper plate is attached to
the moving system of the instruments such that it moves between
the poles of a permanent magnet when the system is oscillating.

39. Critical damping condition
 A ballistic galvanometer will oscillate if it has not been
properly damped (under damped). Galvanometers are
damped by adding a shunt resistor of just the right
amount of resistance in parallel with them. The proper
amount of resistance at which the motion just ceases
to be oscillatory is called the critical external damping
resistance.

40. Summary
• Magnetic field
• Magnetic flux
• Magnetic filed properties
• B on the charged point , current carrying
conductor
• Curl n divergence of magentic field
• Integrel form of ampere’s law
• Ballstic galvanometer and its applications
• Damping conditions of galvanometer

41. Questions :
 Define magnetic flux? Explain the force on a current carrying conductor
 Define magentic filed lines density ? Explain the curl and divergence of
magentic filed
 Define magnetic filed intensity ? Explain the point charge conductor in
magnetic field
 Define galvanometer . Explain the theory of ballastic galvanometer
 Explain critical damping condition of a galvanometer
 Explain current sensitivity and charge sensitivity