The directed flow of charged particles at midrapidity is measured in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV relative to the collision Event Plane, defined by the participant plane using various subdetectors. The rapidity-even directed flow component is measured for the first time using an Event Plane weighted by the transverse momentum of the emitted charged hadrons and found to be largely independent of pseudorapidity with a sign change at transverse momenta $p_{T}$ between 1.2 and $1.7$  GeV/c. These results are compared to measurements made by two other experiments at the LHC. Combined with the observation from ALICE of a vanishing rapidity-even $p_{T}$ shift along the spectator deflection plane is strong evidence for dipole like initial density fluctuations in the overlap zone of the nuclei. These observations open new possibilities for investigation of the initial conditions in heavy-ion collisions with spectator nucleons.