A coaxial cable consists of an inner wire of radius \('a'\) surrounded by an outer shell of inner and outer radii ' \({b}\) ' and '\(c\)' respectively. The inner wire carries an electric current is, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance \({x}\) from the axis when \((i)\) \({x}<{a}\) and \((ii)\) \({a}<{x}<{b}\) ?

1. A \(\frac{{x}^{2}}{{a}^{2}}\)
2. B \(\frac{{a}^{2}}{{x}^{2}}\)
3. C \(\frac{x^{2}}{b^{2}-a^{2}}\)
4. D \(\frac{{b}^{2}-{a}^{2}}{{x}^{2}}\)