We demonstrate that the far-field terahertz beam generated from a Ti:Sapphire two-color laser-induced filament can exhibit a conical or a Gaussian distribution depending on the filtering experimental conditions. Using a 2D electro-optic detection, we provide the first clear evidence that the conical emission in the 0.2-2.6 THz spectral range is due to photo-induced carriers in the silicon filter typically used to block the remaining pump laser light. The low-frequency terahertz beam retrieves an almost Gaussian spatial distribution when the silicon filter is preceded by a large bandgap ceramic filter, which stops the pump beam, preventing carriers generation in silicon.