Principle. When a current is passed through a coil, suspended freely in a magnetic field, it experiences a forces in a direction given by Fleming’s left hand rule.

Construction. It consists of a rectangular coil of thin copper wire wound on a non-metallic frame of ivory. It is suspended by means of a phosphor bronze wire between the poles of a powerful horse-shoe magnet. A small circular mirror is attached to the suspension wire. Lower end of the coil is connected to a hair-spring. The upper end of the suspension wire and the lower end of the spring are connected to terminals T1 and T2. A cylindrical soft iron core (C) is place symmetrically inside the coil between the magnetic poles which are also made cylindrical in shape. This iron core concentrates the magnetic field and helps in producing radial field.

The B.G. is used to measure electric charge. The charge has to pass through the coil as quickly as possible and before the coil stars moving. The coil thus gets an impulse and a throw is registered. To achieve this result, a coil of high moment of inertia is used so that the period of oscillation of the coil is fairly large. The oscillations of the coil are practically undamped.

Theory. (i) Consider a rectangular coil of N turns placed in a uniform magnetic field of magnetic induction B. Lel l be the length of the coil and b its breadth.

Area of the coil = A = lb.
When a current i passes through the coil, torque on the coil = τ = NiBA.            … (1)
If the current passes for a short interval dt, the angular impulse produced in the coil is
                    τ dt = NiBA dt                … (2)
If the current passes for t seconds, the total angular impulse given to the coil is
        ∫^t₀ τ dt = NBA ∫^t₀ i dt = NBAq                    … (3)
Here ∫^t₀ I dt = q = total charge passing through the galvanometer coil.
Let I be the moment of inertia of the coil about the axis of suspension and ω its angular velocity. Then,
Change in angular momentum of the coil = Iω                    … (4)
. :     Iω = NBAq.                                … (5)


(ii) The kinetic energy of the moving system 1/2 Iω² is used in twisting the suspension wire through an angle θ. Let c be the restore torque per unit twist of the suspension wire. Then,
Work done in twisting the suspension wire by an angle θ = 1/2cθ²
. : 1/2I Iω² is used in twisting the suspension wire through an angle θ. Let c be the restoring torque per unit twist of the suspension wire. Then,

Work done is twisting the suspension wire by an angle θ = 1/2cθ²
. : 1/2I Iω² = 1/2c θ² or Iω² = cθ²                                 … (6)

(iii) The period of oscillation of the coil is
    T = 2π √(1/c) or T² = 4π² I/c
. : Multiplying Eqs. (6) and (7), I² ω² = c²T²θ² / 4π²
Or Iω  = cTθ /2π                                         … (8)

Equating (5) and (8), NBAq = cTθ /2π
Or q = (T/2π) (c/NBA) θ                                    … (9)

This gives the relation between the charge flowing and the ballistic throw θ of the galvanometer. q ∞ θ.
(T/2π) (c/NBA) is called the ballistic reduction factor (K).
. : q = K θ   

For more help in Moving Coil Ballistic Galvanometer click the button below to submit your homework assignment.