This paper reports the first measurement of charged particle elliptic flow in Pb-Pb collisions at (s_NN ) = 5.02T eV with the ALICE detector at the CERN Large Hadron Collider. The measurement is performed on more than 20,000 events in 40-50% centrality class on both long-range 2 < || < 4 and short-range || < 1 regions. The two-particle correlation method is used over long-range region, in the transverse momentum range of 1 < p_T < 1.5GeV , and the elliptic flow signals, given by v_n =(V_n ) , are v_2 = 0.17 0.01,v_3 = 0.07 0.01,v_4 = 0.04 0.01,v_5 = 0.03 0.01. Since V_1 is obtained as -0.0013, it does not have a square root value. In addition, for n=2-4, it is found that v_n increases as p_T increases. The Q-vectors method is also used to determine the values of v_2. The magnitudes of the Q-vectors are fitted to a function. The values of v_2 produced by the two methods are compared and discussed. At the end, the vectors are used to analyse high-energy jet particles.
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