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10
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A static charge produces only electric field but moving charge produces both electric field and
magnetic field in space
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Oersted in 1820 AD observed that magnetic field is produced by a current carrying conductor
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Oersted’s experiment : A magnetic compass needle placed in the vicinity of a conductor carrying
conductor aligned perpendicular to the conductor
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Ampere’s swimming rule : Imagine that a man is swimming along the conductor in
i
the direction of the current facing a magnetic needle the north pole of the needle will
deflect towards his left hand
...

i
The direction of magnetic field around the current carrying conductor is given
by
a) Maxwell’s cork screw rule
b) Right hand thumb rule

Maxwell’s cork screw rule : Imagine a right hand screw is advancing in the direction of current in
a conductor
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Right hand thumb rule : Imagine that a current carrying conductor is held in the right hand palm
such that the direction of current is indicated by the thumb
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B
11
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dl along a closed
i r
dl
path round the current carrying conductor is equal to μ o i where i is the current
through the surface bounded by the closed path and μ o permeability of free space
...
dl = μ o i
B 2π r = μ o i

B=

μ oi
2πr

12
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dl
...

;
4π
r2

dB =

μo i

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This law is valid only for small
current segments
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Ampere's law and Biot-Savart law are equivalent but Ampere's law is more useful in some
symmetrical conditions
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The magnetic induction at a point P due to a conductor of finite length is
B=

μ 0i
(sin α + sin β)
4πr

α
β

r

P

i

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The magnetic field induction due to the long current carrying cylindrical conductor is
B=

μ0
ir
⋅
2π (R + r ) 2

Where R is the radius of the conductor and r is the distance of the point from the surface of the
conductor at which the value of B is given
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The magnetic field induction at a point along the axis of a circular coil is
μ
2πnir 2
where n = number of turns, i = current in the coil, r = radius and x = the
B= 0 ⋅ 2
4π (r + x 2 )3 / 2

distance of the point from the centre of the coil
...
e
...

4π x 3

18
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For a solenoid of finite length at any point on the axis
=

μ 0 Ni
[sin α + sin β] ;
2

R

α β

B

L
N is number of turns per unit length
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A solenoid consists of closely wounded helical coil
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The magnetic induction at the centre of the solenoid is B =

μ 0 ni
l

where l is the axial length and n is

total number of turns in length l of the solenoid
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Force on a moving charge in a magnetic field :
2

Electromagnetism
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F = q( v x B) or F = qvB sin θ

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When the charge enters into a uniform
magnetic field perpendicular to its direction, then F = qvB
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24
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Hence no
work is done by it
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When a charged particle moves in a uniform magnetic field at right angles to the direction of the
field
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The direction of force on it due to
the horizontal component of the earth’s magnetic field is towards west
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The force acting on a charged particle when it enters a uniform magnetic field of induction B, with
velocity v at right angles to the field will provide the necessary centripetal force and make the
charged particle move along a circular path of radius ‘r’
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Hence the faster particles move in bigger
circles and slower particles move in smaller circles such that the period of revolution T is the same
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The frequency (ν ) =

qB
2πm

and is called cyclotron frequency
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If a charged particle enters a uniform magnetic field along the line of the field, it goes undeviated
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This force is known as Lorentz force
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The frequency of a charged particle in a uniform magnetic field is known as cyclotron frequency as
the particles in a circular accelerator, called cyclotron, move with this frequency
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Cyclotron is a device used to accelerate charged particles to high speed for nuclear reaction
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The force on a current carrying conductor in a magnetic field :
35
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If the fore finger represents the direction of magnetic field, the middle finger that of current,
then the thumb will represent the direction of force on the conductor
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The total magnetic force on any closed current loop in a uniform magnetic field is zero
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Torque or couple on a current carrying rectangular conductor or loop in a uniform magnetic field is
given by τ = iAB sin θ where A is the area of the rectangular loop, B is the magnetic induction and θ
is the angle between the normal to the plane of the rectangular loop and the field
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e
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When the plane of the
coil makes an angle θ with the field, then the couple acting on the coil is τ = niABCos θ or τ =
MBCosθ
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If i1 and i2 are the strengths of currents passing through two infinitely long, straight and parallel
wires separated by a distance r, the magnetic field induction B, due to the flow of current in the
first conductor at a distance r on the second conductor is B1 =

μ 0 i1

...

2πr

If the current is in the same direction, there will be attraction and if the current is passing in
opposite direction, there will be repulsion
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An ampere is that steady current when flowing in each of two long straight parallel wires separated
by a distance of one metre apart in vacuum causes each wire exert to each other a force of 2x10-7 N
per each metre length of wire
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A moving coil galvanometer consists of a powerful horse shoe magnet with concave poles to
produce
a uniform radial magnetic field
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The plane of the coil always lies in the direction of the
magnetic field because the magnetic field is radial
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i=

Cθ
NAB

ampere

Here C is the couple per unit twist on the suspension fibre, ‘i’ is the current passing through the
galvanometer coil and θ is the angle of deflection by the needle
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Deflection is measured more
accurately using Lamp and Scale arrangement
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The distance between the mirror attached to the suspension fibre of the
galvanometer and the scale is D, then
Tan2 θ ≈ 2θ when 2 θ is very small
Then 2θ =

x
x
; θ=
D
2D

;i=

C
x

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The current sensitivity of a galvanometer is the deflection in mm produced on a scale kept at a
distance of one metre by a constant current of one microampere
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The reciprocal of the current sensitivity is called figure of merit and is expressed in μ A/mm
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A current upto 10–9A can be measured using moving coil galvanometer
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Table Galvanometer : It has a rectangular coil of insulated copper supported on two bearings
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It has a light aluminium pointer which moves on a scale
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The plane of the coil need not be aligned in
magnetic induction
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It is accurate and can be used to measure the
currents of order 10–9 A with proper design
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The
magnetic needle rotates when current is passed
through the coil
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The current flowing in the coil is proportional to
the tangent of deflection
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The galvanometer reduction factor depends on
The galvanometer constant does not depend on
earth’s magnetic field which is different at
earth’s magnetic field
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Stray magnetic fields have no effect on it and
External fields have effect on it and therefore TG
can be used for the measurement of the currents
cannot be used in mines
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Tangent Galvanometer :
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b) works on the principle of Tangent law B= BH Tanθ
Here B = Magnetic induction due to passage of current in the coil =

μ 0i
2r

⎛ 2rB ⎞

c) current measured by Tangent galvanometer is i = ⎜ H ⎟ Tanθ = KTanθ
⎜ μ n ⎟
⎝ 0 ⎠
r = Radius of coil
n = number of turns of coil
d) Reading is more accurate when θ = 45° since relative error

di
1
α
i sin 2θ

and it is minimum for

45°
e) Sensitiveness is maximum when θ = 0° since sensitiveness

dθ
αcos2θ,
di

which is maximum for θ

= 0°
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Shunt :
a) A low resistance connected in parallel to galvanometer to protect it from large current is known
as shunt
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Hence sensitiveness decrease by n times
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Ammeter :
a) It is a device used to measure current in electrical circuits
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c) To increase the range by ‘n’ times or to decrease the Sensitiveness by ‘n’ times , shunt to be
connected across Galvanometer
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g) Among low range and high range Ammeter, low range Ammeter has more resistance
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D
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b) Galvanometer is converted into voltmeter by connecting high resistance in series to it
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D
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f) Among low range and high range voltmeters, high range voltmeter has more resistance
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D
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As series resister value increases sensitivity decreases, accuracy increases

6

V
− G

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