Question

What is radial magnetic field ? Explain principle of moving coil galvanometer with the help of suitable diagram. How can its sensitivity be increased ?

Hint:

The purpose of the radial field is to make the torque (\(\tau = NIAB\sin\theta\)) maximum (\(\theta=90^\circ\)) and independent of the coil's orientation. This results in a linear relationship between current and deflection (\(I \propto \phi\)), which is essential for a calibrated measuring instrument.

Answer 1

1. Radial Magnetic Field:
A radial magnetic field is a magnetic field in which the field lines are always directed along the radii from the center of a circle. In the context of a moving coil galvanometer, it is produced by using cylindrically concave pole pieces of a magnet and placing a soft iron core at the center. This ensures that the plane of the coil is always parallel to the magnetic field lines, and thus the angle between the magnetic field vector (\(\vec{B}\)) and the area vector of the coil (\(\vec{A}\)) is always \(90^\circ\), maximizing the torque.
2. Principle and Working of Moving Coil Galvanometer:
\begin{itemize} \item Principle: The working of a moving coil galvanometer is based on the principle that a current-carrying loop placed in a uniform magnetic field experiences a torque.
\item Working: When a current \(I\) flows through the rectangular coil of \(N\) turns and area \(A\), placed in a magnetic field \(B\), it experiences a deflecting torque (\(\tau_d\)). \[ \tau_d = NIAB \sin\theta \] In a radial magnetic field, \(\theta = 90^\circ\), so \(\sin\theta = 1\). The deflecting torque is maximum and constant for any position of the coil: \[ \tau_d = NIAB \] This torque causes the coil to rotate. As the coil rotates, the suspension wire gets twisted, producing a restoring torque (\(\tau_r\)) that is proportional to the angle of deflection (\(\phi\)). \[ \tau_r = k\phi \] where \(k\) is the torsional constant of the spring. In equilibrium, the deflecting torque equals the restoring torque: \[ NIAB = k\phi \implies I = \left(\frac{k}{NAB}\right) \phi \] Since \((k/NAB)\) is a constant, the current is directly proportional to the deflection (\(I \propto \phi\)). This allows for a linear scale for current measurement.
\end{itemize} Diagram: \begin{center} \begin{tikzpicture} % Poles \node at (-2,0) [left] {N}; \node at (2,0) [right] {S}; \draw[thick] (-1.5,1.5) arc (90:270:1.5); \draw[thick] (1.5,1.5) arc (90:-90:1.5); % Iron Core \draw[fill=gray!30, thick] (0,0) circle (0.8); \node at (0,0) {Soft Iron Core}; % Radial Field Lines \foreach \angle in {45,90,135,225,270,315} { \draw[->, blue] (\angle:0.8) -- (\angle:1.5); } % Coil \draw[red, thick] (0.8,0.5) -- (0.8,-0.5); \draw[red, thick] (-0.8,0.5) -- (-0.8,-0.5); \end{tikzpicture} \end{center} 3. Increasing Sensitivity:
The current sensitivity of a galvanometer is defined as the deflection produced per unit current, \(S_i = \frac{\phi}{I}\). From the equilibrium equation, we have: \[ S_i = \frac{\phi}{I} = \frac{NAB}{k} \] To increase the sensitivity, we can: \begin{itemize} \item Increase the number of turns in the coil (\(N\)). \item Increase the magnetic field strength (\(B\)). \item Increase the area of the coil (\(A\)). \item Decrease the torsional constant (\(k\)) of the suspension fiber by using a material like phosphor-bronze. \end{itemize}