Magnetic Effects & Magnetism

JEE Main level, single correct, medium

65 of 276

Question 65 of 276

A coaxial cable consists of an inner wire of radius aa surrounded by an outer shell of inner and outer radii bb and cc respectively. The inner wire carries an electric current i0{i}_{0} 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 xx from the axis when (i)\left(i\right) x<ax\lt a and (ii)\left(ii\right) a<x<ba\lt x\lt b ?

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Answer: (D) x2a2\dfrac{{x}^{2}}{{a}^{2}}

B1×2πx=μ0I0(x)2a2{B}_{1}\times 2\pi x=\dfrac{{\mu }_{0}{I}_{0}(x{)}^{2}}{{a}^{2}}
B2×2πx=μ0I0{B}_{2}\times 2\pi x={\mu }_{0}{I}_{0}
B1B2=x2a2\dfrac{{B}_{1}}{{B}_{2}}=\dfrac{{x}^{2}}{{a}^{2}}

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