The torque induced beyond the pole shoes in a DC machine is zero. Let's understand why this is the case.

Torque Production in a DC Machine
In a DC machine, the torque is produced due to the interaction between the magnetic field and the current-carrying conductors. This torque is known as the electromagnetic torque.

Working Principle of a DC Machine
A DC machine consists of two main components - the stator (field winding) and the rotor (armature winding). The stator provides the magnetic field, while the rotor carries the current. The interaction between the magnetic field and the current in the rotor produces the torque.

Pole Shoes in a DC Machine
The pole shoes are part of the stator and are used to shape and concentrate the magnetic field. They are made of highly permeable material and are located on the poles of the stator.

Torque Distribution in a DC Machine
The torque in a DC machine is primarily produced at the air gap between the rotor and the pole shoes. This is where the magnetic field from the stator interacts with the current-carrying conductors in the rotor. The torque produced in this region is responsible for the rotation of the rotor.

Torque Induced Beyond the Pole Shoes
Beyond the pole shoes, the magnetic field starts to weaken and spread out. In this region, the magnetic field is not sufficiently strong to interact with the current in the rotor conductors and produce any significant torque. Therefore, the torque induced beyond the pole shoes is practically zero.

Conclusion
In a DC machine, the torque is primarily produced at the air gap between the rotor and the pole shoes. Beyond the pole shoes, the magnetic field weakens, and the torque generation diminishes. Therefore, the torque induced beyond the pole shoes in a DC machine is negligible and can be considered zero.