The needle is considered as a sector of circle with radius r. Now this arrangement of
two quadrants with needle exactly in between, resembles the two capacitors placed side by
side. At equilibrium position, as needle is placed symmetrically, the capacitances യ and C,
are equal. But when needle rotates, the value of one capacitor becomes greater than other.

Let Vv, = Potential of needle, VW = Voltage being measured
V, = Potential of quadrant ‏ہا‎ Va = Potential of quadrant M

Let the needle deflects in anticlockwise direction through an angle ಟಿ.

Let Cc, = Capacitance of left hand capacitor
Cc, = Capacitance of right hand capacitor
d = Distance of needle from either top or bottom plates

of quadrants

⋅ ⊱∶⋀
C= -त --- (1)
Ls)
A = Area of vane = പ =— 0< = 3൭

Note that needle spans through an angle (൨ + 8) under quadrant M and half as there
are two faces of vanes.
5 ‏تمع‎ (൭

5 < = ನ ... (2)

The two capacitances ८1 are in parallel hence,

2

c, = 2c, ‏یہ‎ 8 ... (3)

And, ೬೬೬ (4)
The energy stored का ८1 = 5 ८1 ‏رہ‎ - Vi)”
The energy stored in ८2 = ॐ ‏وح‎ (५७, - Vag”

The total energy stored is,
1 2,1 2
೫೪ = 5011 + न्‌ 2 (छा ~ चोन) (5)

Let T, be the torque in the position @ then for an infinitesimal change ഠ0 of the needle,
the work done in moving system is T, 99. This work done is equal to the increase in the
stored energy dW. ۱

7 നദ്ദ = aw
न aw
5 ಇ = अहं +++ (6)
5 To = ‏ہے عت‎ (५३ - 3 + ‏وه‎ സഘം |
1 dc, 1 dc
ಎ Toe = ‏سے‎ (“1 ಡೀ. സ്യ Se --- ट)
adc, ഒന (൧-൭) er?
Now ae = ‏أ‎ त त
dc, a [ ‏ره عم دمع‎ er2
“ae ~ ‏چو‎ ലി ക്ര