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Two coaxial long solenoids $1 a n d 2$ of same length are set so that one is inside the other. The numbers of turns per unit length are $n_{1} and n_{2} \cdot$ The currents $i_{1}$ and $i_{2}$ are flowing in opposite directions .T h e magnetic field inside the inner coil is zero. This is possible when

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$i_{1} = i_{2} and n_{1} \neq n_{2}$

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

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

$i_{1} \neq i_{2} and n_{1} = n_{2}$

answer is B, D.

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Detailed Solution

Field inside the solenoid $= μ_{0} n i$

So the net magnetic field inside the solenoid is given by,

$B = μ_{0} n_{1} i_{1} - μ_{0} n_{2} i_{2}$

As $B = 0, so n_{1} i_{1} = n_{2} i_{2}$

The above equality can be satisfied by the conditions of option $B a n d D .$

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