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Two coaxial solenoids $1 a n d 2$ of the same length are set so that one is inside the other. The number of turns per unit length are $n_{1} a n d n_{2}$ . The current $i_{1} a n d i_{2}$ are flowing in opposite directions. The magnetic field inside the inner solenoid is zero. This is possible when

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

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

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

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

answer is C, D.

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Detailed Solution

The magnetic field inside the inner solenoid is zero if,

$B_{o u t e r} = B_{i n n e r} o r μ_{0} n_{1} i_{1} = μ_{0} n_{2} i_{2} o r n_{1} i_{1} = n_{2} i_{2} A l s o i f i_{1} = i_{2}, t h e n n_{1} = n_{2}$

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