A charge of +4μC is fixed at point A and a charge of −1μC at point B, 50 cm apart in air. The region from A up to 30 cm towards B is filled with a dielectric slab of relative permittivity 3, while the remaining space is air.
a. (i) Determine the position along line AB, measured from A, at which a unit positive test charge would experience zero net electrostatic force.
b. (ii) State whether this position lies inside the dielectric slab or in the air region.