Statement A : The magnetic force on a current element is non-central because the force Bi dl $\mathrm{Sin}\theta$ is not function of ‘r’.

Statement B : When a solar flare occurs, large number of electrons and protons are ejected by sun, they enter the earth’s atmosphere, collide with atoms and molecules of atmosphere at poles, it results the beautiful display of colours at poles called Auroraboriolis. 

Statement C : Biot-Savart’s law and coulomb’s law both depend inversely on the square of distance but E-field produced by scalar source (charge) and magnetic field produced by a vector source (i dl). 

Statement A: True. Magnetic force on a current element is non-central because it's not solely dependent on the distance 'r' and depends on the current element's orientation.

Statement B: Mostly correct. Solar flares can cause particles to enter Earth's atmosphere, leading to the auroras (Aurora Borealis in the Northern Hemisphere and Aurora Australis in the Southern Hemisphere).

Statement C: True. Both Biot-Savart's law and Coulomb's law depend on distance squared, but electric fields come from scalar sources (charges), while magnetic fields come from vector sources (current elements represented by dl).