Step 1: Understanding the Concept:
The operation of a moving coil galvanometer is based on the torque experienced by a current-carrying loop in a magnetic field.
When current flows through the coil, it experiences a magnetic force that creates a deflecting torque (\(\tau\)).
This torque is countered by a restoring torque from a spring. For the galvanometer to be accurate and easy to read, we want the deflection to be directly proportional to the current.
Step 2: Key Formula or Approach:
The deflecting magnetic torque acting on a loop of \(N\) turns is:
\[ \tau = NIAB \sin \theta \]
Where:
\(A\) is the area of the coil.
\(I\) is the current.
\(B\) is the magnetic field strength.
\(\theta\) is the angle between the normal to the coil plane and the magnetic field lines.
Step 3: Detailed Explanation:
In a uniform magnetic field, the angle \(\theta\) changes as the coil rotates. This would make the torque dependent on the rotation position, resulting in a non-linear (non-uniform) scale.
To prevent this, the pole pieces are made concave (cylindrical) and a soft iron core is placed at the center.
This design forces the magnetic field lines to radiate outward or inward like spokes on a wheel.
Consequently, as the coil rotates, its plane always remains parallel to the magnetic field lines at every position.
If the plane is parallel to the field, the normal vector to the coil face is always perpendicular to the field lines (\(\theta = 90^{\circ}\)).
Since \(\sin(90^{\circ}) = 1\), the torque equation simplifies to:
\[ \tau = NIAB \]
This configuration makes the deflecting torque strictly proportional to the current \(I\) and completely removes any dependence on the angle of rotation. This allows for a clean, linear measurement scale.
Step 4: Final Answer:
The purpose of the radial field is to ensure constant torque regardless of the coil's angular position.