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_1n_1 = i_2n_2`

Answer

C, D

Explanation

`B_("net") = B_1 - B_2 rArr B_1 - B_2 = 0 rArr B_1 = B_2`
` rArr B prop "ni"`. So `n_1i_1 = n_2i_2 " or " n_1 = n_2 " and " i_1 = i_2`