-1-
EXPERIMENT NO. – 8
Helmholtz galvanometer galvanometer AIM - To study the variation of magnetic field with distance along the axis of Helmholtz galvanometer and to estimate the radius of the coil. APPARATUS - Helmholtz galvanometer, magnetometer compass box, ammeter (measure mA), battery eliminator, eliminator, rheostat, commutator, plug ey, ey, connecting wires. THEORY ! The term Helmholtz coils refers to a device for producing a region of nearly uniform magnetic field. "t is named in honor of #erman physicist Hermann von Helmholtz. "t consists of two identical circular magnetic coils that are placed symmetrically symmetrically parallel to each other and on a common common axis, z! axis. axis. The rings rings have radius r and they are separated separated by a distance distance e$ual to or slightly larger than r. %ach coil carries an e$ual electrical current flowing in same direction.
Helmholtz coils The first step to calculate the field of a pair of Helmholtz coil is to calculate magnetic field intensity & produced by each ring. "f a current (") is allowed to flow through a wire of length ( l ), and the wire is bent into an arc of radius r, then the magnetic magnetic field intensity (&) (&) at center of the arc is F =
µ ' Il
(*)
π r where µ ' + permeability of free space (.- x *' !* &m) &or a circular coil of n turns we substitute l+ πrn in e$uation (*) F =
µ ' In
()
r
/ow, substituting substituting the value of µ ' in e$uation () The magnetic field produced by each ring is given by F =
π nI r × *'
0
(1)
The magnetic field at any point on axi at a ditance !x" f#om cente# of coil i
-$π nIr
F = 0
*' ( x
()
1
+ r
)
The #ate of %a#iation of magnetic field&
&igure. 2agnetic field generated by a coil with radius (r) +*m.
&igure1. 2agnetic field generated by a pair of Helmholtz coils Therefore, dF
1 x3(π nir )( x
=−
dx
+ r
d F dx
= ±
r
3 5π nir ( x
= −
+r
)
−
−
-
) 4
−
=
' or
- x (x
+r
&rom which,
x
(
, if
d F dx
dF dx
Thus at point x = ± r from center of coil,
)
−
0
4
=
dF dx
constant.
= constant
6e observe that in figure1, the rate of increase of field due to one coil at midpoint between the coils is e$ual to the rate of decrease of field due to the other at the same point. Therefore if one moves away along the axis from the midpoint, any diminution in the intensity of the field due to one coil is compensated by the increase in the field due to the other so that the field between the coils is practically uniform.
-' The coil is placed in the magnetic meridian, the magnetic field due to the current " flowing in the coil is perpendicular to H (Horizontal component of earth7s magnetic field). Thus the magnetic needle is acted upon by two uniform magnetic fields & and H at right angles to each other. The magnetic needle will mae an angle θ with H in the e$uilibrium position. According to tangent law8 & + H tan θ Therefore
π nIr
tan θ =
(-)
1 0
*' ( x + r ) /ote8 tan θ 9 " tan θ 9 * r 1
MA()ETOMETER* The magnetic compass box used in this experiment is called 2agnetometer. The red point in the magnetometer corresponds to /orth direction (:ed is analogous to positive terminal of electrical circuit.). Thus in absence of magnetic field the needles are in east west direction and while performing the experiment in order to avoid to the %arth7s horizontal magnetic field the bench of the Helmholtz galvanometer should be ept in east!west direction. PRO+E,URE*. The Helmholtz coils should be parallel to themselves and perpendicular to the bench and
at a distance e$ual to r on either side from center of the bench.
.
2agnet compass box is ept at ept at the center of the sliding bench, such that magnetic needle is at the center of the coils. 1. The bench of the Helmholtz galvanometer should be ept in east!west direction . ;ase of the coil is leveled with the help of spirit level and leveling screws. -.
oined to the galvanometer and the other two to the battery through rheostat.
&igure.
-5. Ad>ust the current in the coil with the help of rheostat such that the deflection in the magnetic needle is of the order of - ° at center of bench for both direct and reverse current. 0. /ow move the compass box through cm and note the deflection in east and west direction of magnetometer for direct and reverse current respectively. .
S&n&
,e,eflection in the needle hen it i on one ide of 0ench of +2##ent one +2##ent the needle on ay #e%e#ed Poition
one
of
the
θ *
θ (
θ 1
θ )
cale&
Mea
!,itance of
n
+ompa 0ox cente# coil" x !cm"
*.
'
.
1.
.
5
-.
5.
*'
0.
*
.
*
@.
*5
!deg# ee"
f#om of
%ast end of needle
6est end of needle
%ast end of needle
6est end of needle
Tan
-3*'.
*
**.
'
*.
*1.
*.
5
*-.
*5.
1'
S&)o&
,e,eflection in the needle hen it i on othe# ide of of 0ench the needle +2##ent +2##ent #e%e#ed on one of the one ay Poition
θ *
cale&
θ (
θ 1
θ )
Mea
!,itance of
n
+ompa 0ox cente# coil" x !cm&"
*.
'
.
1.
.
5
-.
5.
*'
0.
*
.
*
@.
*5
*'.
*
Tan deg#
f#om ee
of
%ast end of needle
6est end of needle
%ast end of needle
6est end of needle
-4**.
'
*.
*1.
*.
5
*-.
*5.
1'
(RAPH*
west
east
+A5+U5ATIO)-
:adius of the coil, as obtained from measurement +
Its Circumfere nce (π
(5)
MA6IMUM PRO.A.5E ERROR*- This is obtained by taing logarithmic differentiation of
e$uation (5) RESU5T8 ! *. The variation in the magnetic field with distance, along the axis of the given coil
is as shown in the graph. . :adius of the coil + CCCCCCCCCCcm. as obtained from the graph and CCCCCCCCCCCCCCCcm. as obtained from measurement.
PRE+AUTIO)S*.
-7. usted properly in the magnetic meridian. -. The apparatus should be at considerable distance from current carrying conductors and magnetic materials. 5. The positive mared terminal of the ammeter should be always connected to positive terminal of battery. 0. 6hile taing readings there can be error due to parallax which should be avoided. . :eadings at both ends of the pointer should be taen. SOUR+ES O8 ERROR*.
