Galvanometers
Measuring current with a compass or a twisting coil.
Lesson at a glanceShow the key points
- Tangent law: B = B_H tan θ (36.20).
- Tangent galvanometer: i = K tan θ, K = 2rB_H/μ₀n (36.17); most sensitive near 45°.
- Moving coil: niAB = kθ ⇒ i = (k/nAB)θ (36.18); sensitivity nAB/k.
- Shunt: i_g = R_s i/(R_s + R_g) (36.19).
Two ways to turn a magnetic effect into a current reading: let a compass needle balance a coil’s field against the Earth’s, or let a coil twist against a spring.
The tangent law
A compass needle normally lies along BH. Add a horizontal field B perpendicular to BH: the needle turns to lie along the resultant √(B² + BH²), at angle θ from BH where tan θ = B/BH.
The tangent galvanometer
A vertical circular coil (n turns, radius r) on a levelled base, with a small compass needle at its centre carrying a light aluminium pointer at right angles to it, over a scale marked 0°–90° in each quadrant. A mirror under the pointer removes parallax.
Turn the base until the coil’s plane contains the needle (so it lies in the magnetic meridian) and the pointer reads 0°–0°. Pass the current: the coil’s field μ₀ni/2r at the centre is horizontal and perpendicular to the meridian, so by the tangent law the needle deflects by θ with
The needle should be short compared with the coil, since μ₀ni/2r holds only at the centre.
Sensitivity. Differentiating i = K tan θ: di/i = 2dθ/sin 2θ, so dθ = ½ sin 2θ (di/i). A given fractional change in current moves the needle most when sin 2θ = 1, i.e. near 45°.
A tangent galvanometer has 50 turns of radius 10 cm, where BH = 3.5 × 10⁻⁵ T. What current gives a deflection of 45°?
The moving-coil galvanometer
A rectangular coil of many turns, wound on a soft-iron core, hangs between the poles of a strong permanent magnet by a fine phosphor-bronze strip (from a torsion head), with a phosphor-bronze spring below. A small mirror on the strip reflects a light beam onto a scale. Current enters and leaves through the strip and spring.
The pole pieces are curved (cylindrical) so the field at the coil’s sides always lies in the coil’s plane: the deflecting torque is niAB whatever the angle. The twisted strip pushes back with kθ. At equilibrium:
The soft-iron core strengthens B and so raises the sensitivity (why soft iron does this comes in the next chapter).
A galvanometer coil has 50 turns of area 1.0 cm × 2.0 cm in a field of 0.25 T, on a strip with k = 5.0 × 10⁻⁷ N m/rad. What deflection does 10 µA give?
Protecting it with a shunt
A galvanometer is delicate; too much current damages it. A small shunt resistance Rs in parallel diverts most of the current, leaving
A galvanometer coil of 50 Ω gives full-scale deflection at 5.0 mA. What shunt lets a total of 1.0 A pass at full scale?
- 1Tangent law: B = B_H tan θ (36.20).
- 2Tangent galvanometer: i = K tan θ, K = 2rB_H/μ₀n (36.17); most sensitive near 45°.
- 3Moving-coil: niAB = kθ, i ∝ θ (36.18); sensitivity nAB/k.
- 4Shunt: i_g = R_s i/(R_s + R_g) (36.19).
Check yourself
Keep exploring
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