Along the x -axis, three charges q 2 ,-q and q 2 are placed at x=0, x=a and x=2 a respectively. The resultant electric potential at a point P located at a distance r from the charge -q(a < r) is ( ₀ . is the permittivity of free space)

Step-by-step solution

As r a , so r>2 a So, potential at point P aligned V & = 1 4 ₀ [ q / 2 r+a - q r + q / 2 r-a ] & = 1 4 ₀ q 2 [ 1 r+a - 2 r + 1 r-a ] & = q 8 ₀ [ r(r-a)-2 (r^2-a^2 )+r(r+a) r (r^2-a^2 ) ] & = q 8 ₀ 2 a^2 r (r^2-a^2 ) & = q a^2 4 ₀ r^3 ( as r>a) aligned