ballistic galvanometer The ballistic galvanometer is a suspended moving coil galvanometer with very small damping. It is chiefly used for measuring charge by observing the maximum deflection in its oscillatory motion. For this purpose the time for the charge to pass through the galvanometer should be short compared to the period of oscillation of the coil.

The total effective damping*, b of the galvanometer is given by,

b = b_m + C/R²

where b_m is damping due to the mechanical part, C a constant, and R the total resistance in the circuit. The second term in the right hand side of the equation above arises out of induced emf produced in the coil as it moves in the magnetic field of permanent magnets. This impedes the motion of the coil, and is called electromagnetic damping. This can be reduced by increasing R. When the coil oscillates with open circuit, R is infinity and electromagnetic damping vanishes.

When a charge Q passes through the galvanometer, its effect is an impulse on the coil. The rotation of the coil through an angle q is proportional to the charge Q. A mirror fixed on the plane of the coil reflects light from a lamp and scale arrangement kept 1m away from the galvanometer on the scale of the arrangement. The deflection d₁ of the light spot on the scale is proportional to the rotation of the coil for small angle of rotation. The relationship between the charge Q and d₁ is given by,

Q = [KT/(2p )] d₁ [coulomb]

where T is the time period of oscillation of the coil and K, the figure of merit of the galvanometer.

K=k/(NAB2L)

where k is torque constant of the wire of suspension of the coil, N the number of turns, A the area , B the magnetic field produced by the magnets, and L the distance between lamp and galvanometer (1 m). The figure of merit of the galvanometer is obtained by taking the ratio of steady current i and the corresponding deflection of the light spot.

The actual deflection produced is smaller due to the presence of damping. The size of the correction can be found by measuring the logarithmic decrement, l of the successive swings on the same side.

l = ln(q ₁/ q ₃) = ln(q ₃/ q ₅) = …

l = ln(d₁/ d₃) = ln(d₃/ d₅) = …

Corrected deflection d₀ is given by,

d₀ = d₁ e l ^{/ 4}

Or since l is small,

d₀ = d₁ (1+ l /4) = d₁ + (d₁ – d₃)/4

The ability of ballistic galvanometer to measure charge accurately, is employed for measuring high resistances, capacitances, magnetic field etc.