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Q.

A coaxial cable is made up of two conductors. The inner conductor is solid and is of radius R₁ and the outer conductor is hollow of inner radius R₂ and outer radius R₃. The space between the conductors is filled with air. The inner and outer conductors are carrying currents of equal magnitudes and in opposite directions. Then the variation of magnetic field with distance from the axis is best plotted as

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a

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b

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c

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d

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answer is C.

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Detailed Solution

From ampere's law the field at the axis is zero. From x = zero to R₁, the field increases linearly as the charge enclosed increases. From x = R₁ to R₂ and from x = R₂ to R₃, the field decreases hyperbolically but with different slopes as the media are different. Hence the required graph is.

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$B = \{\begin{array}{ccc} \frac{μ_{0}}{2 π} \frac{ir}{R_{1}^{2}} & for & r \leq R_{1} \\ \frac{μ_{0}}{2 π} \frac{i}{r} & for & R_{1} \leq 2 r \leq R_{2} \\ 0 & for & r > R_{3} \end{array}$

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A coaxial cable is made up of two conductors. The inner conductor is solid and is of radius R1 and the outer conductor is hollow of inner radius R2 and outer radius R3. The space between the conductors is filled with air. The inner and outer conductors are carrying currents of equal magnitudes and in opposite directions. Then the variation of magnetic field with distance from the axis is best plotted as