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?
[Roorkee 2000]

• A. $i_1\ne i_{2}and{n}_1=n_2$
  
• B. $i_1=i_{2}and{n}_1\ne n_2$
  
• C. $i_1=i_{2}and{n}_1=n_2$
  
• D. $i_1{n}_1=i_2{n}_2$

Answer 1

Answer: (C), (D)

$i_1{n}_1=i_2{n}_2$

$B_{net}=0\Rightarrow B_1-B_2=0\Rightarrow B_1=B_2$
$\Rightarrow B\propto ni$. So $n_1{i}_1=n_2{i}_2$ or $n_1=n_2$ and $i_1=i_2$