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Two very long, coaxial solenoids 1 and 2 are set so that one is inside the other. The number of turns per unit length are $n_{1}$ and $n_{2}$ . The currents $i_{1}$ and $i_{2}$ respectively are flowing in them in opposite directions. The magnetic field at the axis of coils is zero. This is possible when

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$i_{1} \neq i_{2} a n d n_{1} = n_{2}$

$i_{1} = i_{2} a n d n_{1} \neq n_{2}$

$i_{1} = i_{2} a n d n_{1} = n_{2}$

$i_{1} n_{1} = i_{2} n_{2}$

answer is C, D.

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Detailed Solution

$B_{n e t} = B_{1} - B_{2} \Rightarrow B_{1} - B_{2} = 0 \Rightarrow B_{1} = B_{2} \Rightarrow B α n i .$

So, $n_{1} i_{1} = n_{2} i_{2}$ or $n_{1} = n_{2}$ and $i_{1} = i_{2}$

$∴$ options (c) and (d) are correct.

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