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 $(ii)$ ${a}<{x}<{b}$ ?

Q: 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 $(ii)$ ${a}<{x}<{b}$ ?

a when ${x}<{a}$ ${B}_{1}(2 \pi {x})=\mu_{\circ}\left(\frac{{i}_{\circ}}{\pi {a}^{2}}\right) \pi {x}^{2}$ ${B}(2 \pi {x})=\frac{\mu_{\circ} {i}_{\circ} {x}^{2}}{{a}^{2}}$ ${B}_{1}=\frac{\mu_{\circ} {i}_{\circ} {x}}{2 \pi {a}^{2}}...(1)$ when ${a}<{x}<{b}$ ${B}_{2}(2 \pi {x})=\mu_{0} {i}_{0}$ ${B}_{2}=\frac{\mu_{{o}} {i}_{\circ}}{2 \pi {x}}...(2)$ $\frac{{B}_{1}}{{B}_{2}}=\frac{\mu_{\circ} {i}_{\circ} \frac{{x}}{2 \pi {a}^{2}}}{\frac{\mu_{\circ} {i}_{\circ}}{2 \pi {x}}}=\frac{{x}^{2}}{{a}^{2}}$

Question

A$\frac{{x}^{2}}{{a}^{2}}$
B$\frac{{a}^{2}}{{x}^{2}}$
C$\frac{x^{2}}{b^{2}-a^{2}}$
D$\frac{{b}^{2}-{a}^{2}}{{x}^{2}}$

JEE MAIN 2021, Diffcult

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