A particle of charge q and mass m is subjected to an electric field
E = E₀ (1 – $$a$$x²) in the x-direction, where $$a$$ and E₀ are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :

A two point charges 4q and -q are fixed on the x-axis at x = $$ - {d \over 2}$$ and x = $${d \over 2}$$ respectively. If a third point charge 'q' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will :

Two charged thin infinite plane sheets of
uniform surface charge density $${\sigma _ + }$$ and $${\sigma _ - }$$,
where |$${\sigma _ + }$$| > |$${\sigma _ - }$$|, intersect at right angle.
Which of the following best represents the
electric field lines for this system :

Concentric metallic hollow spheres of radii R and 4R hold charges Q₁ and Q₂ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :