Physics · Ch 3 — Magnetism and Magnetic Effects of Electric Current
Tangent Law and Tangent Galvanometer
Tangent Law and Tangent Galvanometer
A tangent galvanometer is a moving-magnet instrument used to detect small currents, built around the tangent law: when a magnetic needle is freely suspended in two mutually perpendicular uniform fields, it settles along their resultant, making an angle with one of them such that
The instrument consists of a many-turn copper coil wound on a non-magnetic vertical frame mounted on a levelled turntable, with a small pivoted compass needle exactly at the coil's centre (so the coil's field and the needle's centre coincide). Its precautions: keep other magnets away; level the base so the needle is horizontal and the coil vertical; rotate the coil about its vertical axis so its plane contains the needle (i.e. lies in the magnetic meridian); and rotate the compass box alone so the pointer reads – with no current flowing.
With no current, the needle rests along . Once current flows, the coil's own field (normal to the coil's plane, from , §3.8.3) acts perpendicular to , and the needle deflects to angle given by the tangent law. Combining the two relations, …
What this figure shows. A circular coil is mounted vertically on a horizontal turntable with three levelling screws, and a small compass box sits at the exact centre of the coil, containing a pivoted magnetic needle with an aluminium pointer that sweeps over a circular scale graduated in four quadrants from 0 to 90 degrees, with a mirror underneath the pointer to avoid p …
What this figure shows. The compass needle at the centre of the tangent galvanometer's coil is shown deflected by angle theta away from its rest position along BH (the horizontal component of Earth's field, drawn horizontally) toward B (the field produced by the current in the coil, drawn perpendicular to BH, i.e. normal to the plane of the coil) -- the needle settles along the vector sum of these two mutuall …
Worked out. A tangent galvanometer coil of diameter 0.24 m (radius 0.12 m) with N=100 turns sits where BH = 25x10^-6 T, and gives a deflection of 60 degrees, so tan(60)=1.732. Combining the coil-field formula B=mu0 N I/(2R) with the tangent law B=BH tan(theta) gives I = 2 R BH tan(theta)/(mu0 N) = (2 x 0.12 x 25x10^-6 x 1.732)/(4 pi x10^-7 x 100), which works out to I approx 0.082 A -- illustrating exactly how a tangent galvanometer's scale reading is converted into an actual current value using its own kn …