Two point charges +4μC and −9μC are fixed 50cm apart on a straight line in vacuum. Take the +4μC charge at the origin O and the −9μC charge on the positive x-axis.
a. (i) For a small positive test charge q placed at a point P on the x-axis at coordinate x, write an expression for the net electrostatic force F(x) acting on it in terms of x.
b. (ii) Obtain all value(s) of x (if any) for which F(x)=0.
c. (iii) Identify which of the positions found in part (ii) are physically accessible to the test charge and give reasons for rejecting any non-physical solutions.