Question

Two coaxial solenoids 1 and 2 of the same length 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 $i_2$ are flowing in opposite directions. The magnetic field inside the inner coil is zero. This is possible when

• A. $i_1\ne i_2$ and $n_1=n_2$
• B. $i_1=i_2$ and $n_1\ne n_2$
• C. $i_1\ne i_2$ and $n_1=n_2$
• D. $i_1{n}_1=i_2{n}_2$

Answer 1

The correct option is D $i_1{n}_1=i_2{n}_2$

For magnetic field inside the solenoid to be zero,
$B_1=B_2$
Here, $B_1$ and $B_2$ are the magnetic fields inside the inner cores dues to solenoids 1 and 2 respectively.

${\mu }_0{n}_1{i}_1={\mu }_o{n}_2{i}_2$
$n_1{i}_1=n_2{i}_2$