Two coaxil 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 current `i_(1)` and `i_(2)` are flowing in opposite directions. The magnetic field inside the inner coil is zero. This is possible when

Options

A. `i_(2)cancel(=)i_(2)` and `n_(1)=n_(2)`
B. `i_(2)=i_(2)` and `n_(1)cancel(=)n_(2)`
C. `i_(2)=i_(2)` and `n_(1)=n_(2)`
D. `i_(1)n_(1)=i_(2)n_(2)`

Answer

3,4

Explanation

`B_(n et)=B_(1)-B_(2)implies B_(1)-B_(2)=0impliesB_(1)=B_(2)`
`impliesB prop ni`. So `n_(1)i_(1)=n_(2)i_(2)` or `n_(1)=n_(2)` and `i_(1)=i_(2)`