Question
A circular coil of thin insulated copper wire (N = 2000 turns), wrapped around an iron cylinder of cross-section area ΔS = 0.001 m2, is connected to a suspended type moving coil ballistic galvanometer. The suspended rectangular coil of the galvanometer has length ℓ = 5 cm, breadth b = 3 cm and n = 100 turns, moment of inertia I = 2.7 × 10−6 kg m2 about the vertical axis, and hangs from a fiber of torsional constant c = 3.0 × 10−3 N m/rad in a radial magnetic field B = 0.1 T. The charge pulse is much shorter than the coil's period and damping is negligible, so q = (T/2π)(c/nAB)θ, where A = ℓ × b and θ is the angle turned by the coil. When the magnetic induction of 1.0 T, perpendicular to the plane of the circular coil, is reversed, the spot of light reflected from a mirror on the suspension moves 40 mm on a scale 1.0 m from the mirror (the reflected ray turns through twice the coil's angle). The correct statements are
Options
Solution
T = 2π√(I/c) = 0.188 s ≈ 0.19 s.
The flux linkage changes by 2NBΔS = 4.0 Wb-turn. θ = 0.040/(2 × 1.0) = 0.02 rad
gives q = (T/2π)(c/nAB)θ = 120 μC,
so C is false, and R = 4.0/(120 × 10−6) = 33.3 kΩ.
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