Figure shows three arrangements of electric field lines. In each arrangement, a proton is released from rest at point P and then accelerated through point Q by the electric field. Points P and Q have equal separations in the three arrangements. If p₁ p₂ and p₃ are linear momentum of the proton at point Q in the three arrangement respectively, then

Step-by-step solution

The work done by the electric field on a proton moving from point P to point Q is given by W = _ P ^ Q F d r = q _ P ^ Q E d r . By the work-energy theorem, the change in kinetic energy is equal to the work done, so K = K_Q - K_P = W . Since the proton is released from rest at P, K_P = 0 , thus K_Q = W = p^2 2m , which implies p = 2m W . The work done W is equal to q V , where V is the potential difference between P and Q. The potential difference is V = _ P ^ Q E d r . In arrangement 1, the electric field lines ar