Tungsten itself is not magnetic, as it is a diamagnetic material, which means that it is not attracted to a magnetic field. Therefore, pure tungsten needles are not magnetic.
However, if the tungsten is alloyed with other metals such as iron, cobalt, or nickel, the resulting alloy can exhibit magnetic properties. For example, tungsten carbide, which is a common tungsten alloy used in industrial applications, can be magnetic due to the presence of iron in its composition.
In general, the magnetic properties of tungsten needles will depend on their composition and any other materials that they may be in contact with. Pure tungsten needles are not magnetic, but if they are alloyed with magnetic materials, or if they come into contact with magnetic fields or other magnetic materials, they may exhibit magnetic properties to some extent.