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_(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

C, D

Explanation

The magnetic field inside the inner solenoid is zero if `B_("outer")= B_("inner") or mu_(0)n_(1) i_(1)= mu_(0) n_(2)i_(2)`
or `n_(1)i_(1)= n_(2)i_(2)`
Also if `i_(1)= i_(2)`, then `n_(1)= n_(2)`