A nozzle assembly of a fuel injector comprising: a nozzle with a body extending along a main axis, said body having a peripheral wall and defining an internal bore in which a needle is axially moveable between a closed position, in which a first end of said needle rests on a valve seat to prevent fuel injection through one or more injection orifices of said nozzle, and an open position in which said needle is lifted from said seat to allow injection; wherein said needle extends along a needle axis and has an overall shape with symmetry of revolution about said needle axis, said needle comprising a shaft portion which is tapered at said first end and defines an annular seating face cooperating with a seating face on said valve seat; wherein said nozzle assembly further includes a detection circuit in which said needle forms a switch; wherein said needle is designed to include a local dissymmetry in the region of said annular seating face, which is configured to cause, in use, an unbalance of forces resulting in a transversal force exerted by the fuel about said needle first end and, wherein said tapering first end includes an intermediate section (34.1) connected at one end to said needle shaft portion and at the other end to a conical section (34.2) defining said annular seating face, wherein said conical section (34.2) is configured to define a contact line in a plane substantially perpendicular to said needle axis, characterized in that said local dissymmetry is located adjacent said contact line, on the side of said intermediate section (34.1), wherein said conical section (34.2) has circular symmetry about said needle axis except over a predetermined angular section that is less than 180° and, wherein said local dissymmetry is formed by a truncated peripheral portion of said conical section, for example removed by machining. a nozzle with a body extending along a main axis, said body having a peripheral wall and defining an internal bore in which a needle is axially moveable between a closed position, in which a first end of said needle rests on a valve seat to prevent fuel injection through one or more injection orifices of said nozzle, and an open position in which said needle is lifted from said seat to allow injection; wherein said needle extends along a needle axis and has an overall shape with symmetry of revolution about said needle axis, said needle comprising a shaft portion which is tapered at said first end and defines an annular seating face cooperating with a seating face on said valve seat; wherein said nozzle assembly further includes a detection circuit in which said needle forms a switch; wherein said needle is designed to include a local dissymmetry in the region of said annular seating face, which is configured to cause, in use, an unbalance of forces resulting in a transversal force exerted by the fuel about said needle first end and, wherein said tapering first end includes an intermediate section (34.1) connected at one end to said needle shaft portion and at the other end to a conical section (34.2) defining said annular seating face, wherein said conical section (34.2) is configured to define a contact line in a plane substantially perpendicular to said needle axis, characterized in that said local dissymmetry is located adjacent said contact line, on the side of said intermediate section (34.1), wherein said conical section (34.2) has circular symmetry about said needle axis except over a predetermined angular section that is less than 180° and, wherein said local dissymmetry is formed by a truncated peripheral portion of said conical section, for example removed by machining. wherein said conical section (34.2) has circular symmetry about said needle axis except over a predetermined angular section that is less than 180° and, wherein said local dissymmetry is formed by a truncated peripheral portion of said conical section, for example removed by machining.