Question

Why do we use concave magnetic pole in the galvanometer

Answer 1

The concave cylindrical poles provide a radial magnetic field. In a radial magnetic field the coil is always parallel to the field and therefore the torque experienced by the coil is always maximum, ... The magnet of a galvanometer is a horseshoe laminated magnet with concave pole faces.

Answer 2

The cylinder is a pole piece of the magnet, just as the concave shapes are. The induction of the winding is hoop-like, not radial at all. So, the cylinder makes the permanent magnet field nearly radial, not the 'field of the coil', but the permanent magnet field that permeates the space in which the coil moves. Without field shaping, a dipole field and coil would give sine(theta) dependence on current, instead of (roughly) theta dependence.