M
Moving C
Coil Galvaanometeer
Moving coil Galvano
ometer: Principle
e :( Based on
n the principle of the forcce of interacction betweeen the curren
nt carrying co
onductor and a m
magnetic field
d) A coil is su
uspended in a magnetic field. The current to bee measured iis passed through the coil. Th
he current th
hrough the coil produce
es a magnetic field whicch interacts with the pended. Due to the interaaction the co
oil gets deflected and given magnetic field in which thee coil is susp
measuring the anglee of rotation current can be calculate
ed. A circcular or rectaangular coil of about 10 to 15 turns of a fine insulaated copperr or aluminiium wire is suspended from a torsio
on head T, by means of o quartz fib
bre in between the concaave pole piecces of a stron
ng magnet. TThe lower en
nd of the coil iss attached to
o a light sprin
ngs which brrings the coill back to its original o
position when the curren
nt is stoppe
ed. The suspeension wire and the sp
pring are co
onnected with w
two termiinal screws at the basse which accts as the leads l
of current. The who
ole thing is enclosed in a metal box p
provided nd is supportted on levelin
ng screws. Th
he angle with gglass face an
of ro
otation of the coil is measured by lamp & & scale arran
ngement, refflection takees place from
m the tiny mirror m
M attached with the
e suspension
n wire. Theory
y : Given n = the numberof turnsin thhecoil
l & b= the length
l
of eacch vertical & horizontalside
s of the cooil respectivvely ( assuminng) the coil to
t be rectanggular
i = the curreentflowingthrough
t
the coil.
c
B = the induuctionvectoorof the maggneticfield inn which the coil
c is suspeended.
We know thhat theforceeexperienced by thecurreentcarryinggconductorpllacedin a maagneticfieldd is
( )
F = i l × B → (1)
Force onn each wire' de' and ' fc'
F = ibB
B sin(90 − φ ) = ibB sin φ
p
of thee coil and thee direction off the magneeticfield.
whereφ = angle bettween the noormal to the plane
he wires ' de' & ' fc' are in the plane off the coil alo
ong the down
nward
The direection of thee force on th
and upw
ward directioon respectively and hencce cancel outt.
©SelfStu
udy.in IEMS ‐ H
High School T
Tutorial Classs Notes Curreent Electricityy Page 1 M
Moving C
Coil Galvaanometeer
The forcce on the two
o vertical wirres ‘cd’ and ‘‘ef’ by using equation (1)) are found tto have magn
nitude 0
F = ilBsin90 = ilb
Applyingg the right h
hand curl rule for vector product the
e directions of the force are as show
wn in the figure. TThese two fo
orces being eequal in maggnitude, opp
posite in direection paralleel and non cco‐planer constitute a couple. Momen
ntof the coup
ple Γ = ilB × OC
Γ = ilBbbsinφ = i(lb) B sinφ = iA
ABsinφ
Since thhereare n turrnsin thecoil the total torrqueexperieenced by thecurrent
c
carryyingcoil in thhe magneticfield
f
Γ = niA
ABsinφ
Due to tthis torque th
he coil rotatees a restoring couple due
e to the torsion rigidity sets in and when the restoring couple equ
uals to the deeflecting cou
uple the coil comes to eq
quilibrium Letc = torsionalcou
upleper unit twistof thesuuspensionwiire
gh w
hich thecoil
c rotatein the
t positionof
o equilibriuum
θ = theeanglethroug
Restoringcouple= cθ → (1)
Fromeqquation(2
) an
nd(3): nAiBsinφ = cθ
c θ
→ (4)
nAB
B sinφ
By usinngconcavepo
olepiecestheemagneticfieeldis made
i=
radialsoo thatfor any
ypositionof coil
c φ is alwaays900 ,
sinφ = sin
s 900 = 1
c
θ → (5)
AB
nA
Sincec,,n,A & B areeallconstant
∴i =
i ∝θ
©SelfStu
udy.in IEMS ‐ H
High School T
Tutorial Classs Notes Curreent Electricityy Page 2