Torque on a Current Loop — Question 7

Question 7

A radial-field moving-coil instrument has a linear current-to-angle scale

A moving-coil instrument is designed so that its active conductors remain perpendicular to a radial gap field and its torque is $\tau_B=NIAB$ throughout the useful angle range. A spring provides restoring torque kappa theta.

1. Derive the equilibrium deflection per unit current.

2. If the allowed deflection is thetaMax, derive the full-scale current. Explain why the field geometry avoids the cosine factor of a coil turning in a spatially uniform field.

Question 7 - Solution

A radial-field moving-coil instrument has a linear current-to-angle scale

(a) Method and calculation

$$\kappa\theta=NIAB\Rightarrow\theta=\frac{NAB}{\kappa}I.$$$$\frac{d\theta}{dI}=NAB/\kappa=\text{constant}.$$

(b) Interpretation and further calculation

$$I_{\mathrm{FS}}=\frac{\kappa\theta_{\max}}{NAB}.$$$$\tau_B/(NIAB)=1\quad\text{throughout the designed range}.$$The radial geometry maintains the maximum local force lever arms instead of a fixed external field direction.

Physical check

The stated torque law is a property of the radial-gap design, not of an arbitrary uniform field.