Magnetism and electro-magnetism
2nd Year Physics Notes
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MAGNETISM AND ELECTRO-MAGNETISM
MAGNETIC FIELD DUE TO CURRENT
It was discovered by Oersted that when current masses through a
conductor, magnetic field is produced. This field is known as "Magnetic
Field of Induction" and is denoted bu "B".
Ampere found that when two current carrying conductors are near each
other, they experience force at each other. If the current is in the
same direction the force is attractive and if the current is in
opposite direction.
When electric charges are at rest they exert electrostatic force of
attraction or repulsion on each other. When the charges are in motion
they exert electric as well as magnetic force on each other because and
isolated moving positive and negative charge create both electric and
magnetic field.
MAGNETIC FIELD
Magnetic Field is a space or region around a magnet or current
carrying coil of wire where its effect can be felt by small compass
needle. Magnetic field of induction can be visualized by magnetic lines
of induction.
A line of induction is an endless curve, which can be traced by a compass needle.
MAGNETIC FLUX AND FLUX DENSITY
The total number of magnetic lines of induction passing through a surface is called magnetic flux.
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DETERMINING THE CHARGE TO MASS RATIO OF AN ELECTRON
The charge to mass into of an electron was determined by Sir J.J.
Thomson by an apparatus which consists of a highly evacuated pear shaped
glass pulls into which several metallic electrodes are sealed.
Electrons are produced by heating a tungsten flament F by passing a
current through it. The electrons moving sideways are also directed
towards the screen by applying negative potential on a hollow cylinder C
open on both the sides surrounding the filament. Electrons are
accelerated by applying positive potential to discs A and B. If V be the
total total P.d between the disc Band the filament F taken then
Kinetic Energy.
The beam strikes the screen coated with zinc sulphide after passing
through the middle of the two horizontal moetal P'P and a spot of the
light produced at O on the screen where the beam strikes and its
position is noted.
A magnetic field of induction B is produced in between the plate
directed into the paper. The magnetic field is produced by two identical
current carrying coils placed on either side of the tube at the
position of plates.
The force due to the magnetic field on the moving electron makes them
move in a curved path and the light spot shifts from O to O on the
screen there from of magnetic field acts as centripetal force
e. V B = mv2 / r
e/m = V/Br -------- I
e/m can be computed if the radius r and the expression of the circular
path are in which the beam moves in the field region is determined. The
radius r is calculated from the shift of the light spot i.e. r = 3.
A better method of determined V is as under. An electric field E is
produced between the plates by applying suitable potential difference
to exert a force "Be" on the electron opposite to that due to the
magnetic field.
The potential diff. VI is so adjusted that two fields neutralize each
other effects and the spot come back to its initial position O. Thus
each other effects and the spot come back to its initial position O.
Thus
Ee = Be V
Or
V = E/B ----- (II)
Where E = V1 / d
d = distance between the plates.
Putting the value of V from eq 2 in 1
e/m = E/B2r
e/m = K75888 x 10(11) e/kg
AMPERE'S LAW
According to this law the sum of the product of the tangential
component of the magnetic field of indaction and te length of an element
of a closed curve taken in a magnetic field is μo times the current
which passes through that area bounded by the curve.
Consider a long straight wire carrying a current 1 in the direction.
The lines of force are concentric circles with their common centre on
the wire. From these circles consider a circle of radius r. The
magnitude of the magnetic field at all points on this circle and inside
the circle is same.
Biot and Savart experimentally found that the magnitude of the field
depends directly on twice the current and inversely proportional to the
distance r from the conductor.
SOLENOIDAL FIELD
A solenoid is a coil of an insulated copper wire wound on a circular
cylinder with closed turns. When current passes through it, magnetic
field is produced with is uniform and strong inside the solenoid while
outside it the field is negligibly weak.
Consider a solenoid through which the current 1 is passing in order to
determine the magnetic field of induction B at any point inside the
solenoid imagine a closed path "abcda" on the form of a rectangular.
The rectangular is divided into four elements of length L1, L2, L3, L4.
L1 is along the axis inside the solenoid and L3 is far from the
solenoid.
By applying amperes circuital law
B L1 + B. L2 + L2 + B. L3 + B. L4 = μo x current enclosed ----- (I)
Since B. L1 is parallel inside the solenoid
B. L1 = BL4 cos 0 = BL4
The field is very weak outside the solenoid is very weak and therefore it can be negnected thus
B. L3 = 0
As B is perpendicular to L2 and L4 inside the solenoid therefore
B. L2 = BL2 cos 90 = 0
B. L4 = BL4 cos 90 = 0
substitute the above values is eq 1
B. L1 + O + 0 + 0 = μo x current closed
B. L1 = μo x current enclosed ------- (II)
If there are n turns per unit length of the solenoid and each turn carries a current I will be "n L1I"
TOROIDAL FIELD
A Toroid or a circular solenoid is a coil of insulated copper wire
wound on a circular core with close turn. When the current passes
through the toroid, magnetic field is produced which is strong enough
inside while outside it is almost zero.
Consider a toroid that consists of N closely packed turns that carry a
current I. Imagine a circular curve of concentric the core.
It is evident form of the symmetry at all points of the curve must have
the same magnitude an should be tangential to the curve at all points.
Divide the circle into small elements each of length ΔL is so small
that B and ΔL are parallel to each other.
By amperes law
Σ B : ΔL = μo x current enclosed
ΣB ΔL Cos 0 = μo x current enclosed
ΣB ΔL = μo x current enclosed
BΣ ΔL = μo x current enclosed
Σ ΔL = 2 π r
B 2 π r = μo x current enclosed -------- (I)
Cases
If the circular path 1 is outside the core on the inner side of the toroid if enclose no current. Thus eq 1 become
B 2 π r = μo x 0 = 0
B = 0
If the circular path 2 is outside the core on the outer side of the
toroid each turn of the winding passes twice through the area bounded
by this path carrying equal currents in opposite directions thus the
net current through the area is zero hence eq 1 becomes
B 2 π r = μo x 0 = 0
B = 0
If the circular path 3 is within the core the area bounded by the curve
will be threaded by N turns each carrying 1. Thus Current enclosed =
NI
Therefore eq 1 becomes
B 2 π r = μo NI
B = μo NI / 2 π r
ELECTROMAGNETIC INDUCTION
The phenomenon in which an Emf is set up in a coil placed in a
magnetic field whenever the flux through it is changing is called
ELECTROMAGNETIC INDUCTION. If the coil forms a part of a closed circuit
the induced Emf cases a current to flow in the circuit. This current is
called INDUCED CURRENCY.
The magnitude of induced emf depends upon the rate at which the flux
through the coil charges. It also depends on the number of turns on the
coil.
The magnetic flux through a circuit can be changed in a number of
different ways. By changing the relative position of the coil w.r.t to a
magnetic field or current bearing solenoid.
By changing current in the neighbouring coil or by changing current in the coil itself.
By moving a straight conductor in the magnetic field in such a way that it cut the magnetic lines of force.
FLUX LINKAGE
The product of number of turns N and the flux Ñ„ through each turn of the coil is called flux linkage i.e.
Flux Linkage = N Ñ„
FARADAY'S LAW OF ELECTROMAGNETIC INDUCTION
A Emf is induced in a coil through which the magnetic flux is
changing. The Emf lasts so long as the change of flux is in progress and
becomes zero as soon as the flux through the coil becomes constant or
zero.
SELF INDUCTION
Consider a coil through which an electric current is flowing. Due to
this current magnetic field will be produced which links with the coil
itself. If for any reason the current changes the magnetic flux also
changes and hence an Emf is induced in the coil this phenomenon is known
as SELF INDUCTANCE. In accordance with Lenz Law, the emf posses the
change that has induced it and it is therefore known as back emf.
If the current is increasing the back emf opposes the increase. If the current decreasing it opposes the decrease.
The back emf is directly proportional to the rate of change of current. If ΔL change in current Δ t then back emf E is given.
e = L Δl / Δt ------- (I)
Where L = self inductance of the coil.
The measure of the ability of a coil to give rise to a back emf is
called the Self inductance. Its value depends on the dimensions of the
coil, the number of turns and the permeability of the core material.
Its unit is henry.
Henry
The self inductance of a coil is 1 Henry if the current varying through
is at the rate of 1 amp/sec, induces a back emf of 1 volt.
If N be the number of turns in the coil and Δ φ be the change of flux in time Δ t then by Faraday's Law.
Є = -N Δφ / Δt ----- (II)
-N Δφ / Δt = - Δl / Δt
N Δφ = L Δl
Δ (Nφ) = Δ (Ll)
Nφ = L1
MUTUAL INDUCTION
Consider two coils close to each other. One coil is connected to a
source of emf and the other with a galvanometer. The coil which is
connected to the emf is called the primary coil and the other is called
secondary coil. Some of the magnetic flux produced by the current in
the primary coil is changed the magnetic flux in the secondary coil
also changes and hence an emf is induced in the secondary this
phenomenon is called mutual induction.
The back emf "ξ" induced in the secondary coil is directly proportional
to the rate of change of current Δ1 / Δt in primary coil and is given
by
Є2 = -M ΔI / Δt -------- (I)
Where M is the mutual inductance of the pair of coils. Its value
depends upon the number of turns of the coil, their cross-sectional
area, their closeness and core material. Its unit is Henry.
If N2 be the number of turns in the secondary and Δф / Δt be the rate of change of flux in it then by faraday's law.
Є2 = -N2 Δφ2 / Δt ------ (II)
Comparing 1 and 2
-N2 Δφ2 / Δt = - M Δ1 / Δt
N2 Δφ2 = M Δ1
Δ(N2 φ2) = Δ(M 1)
N2 φ2 = M 1
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Non-Inductive Winding
In bridge circuits such as used for resistance measurements self inductance is a nuisance.
When the galvanometer key of bridge is closed the current in the arms
of bridge are re-distributed unless the bridge happens to the balanced.
When the currents are being re-distributed these are changing and self
induction delays the reading of new equilibrium. Thus the galvanometer
key thus not corresponds to steady state which the bridge will
eventually reach. Its me therefore be misleading.
To minimize their self inductance coils of the bridge and re-resistance
boxes are so wound as to setup extremely small magnetic field.
The wire is doubled back on itself before being coiled.
In this type of winding current flows in opposite direction in the
double wires and consequently the magnetic field and hence the magnetic
flux setup by one wire in neutralized by that due the other wire.
Hence self induced emf will not be produced when the current through
the circuit changes.
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2nd Year Physics Notes