question_answer

There are two long co-axial solenoids of same length \[l\]. The inner and outer coils have radii \[{{r}_{1}}\] and \[{{r}_{2}}\]and number of turns per unit length \[{{n}_{1}}\] and \[{{n}_{2}}\] respectively. The ratio of mutual inductance to the self inductance of the inner- coil is-         [JEE Main 11-Jan-2019 Morning]

A) \[\frac{{{n}_{2}}}{{{n}_{1}}}\]

B) \[\frac{{{n}_{2}}}{{{n}_{1}}}.\frac{r_{2}^{2}}{r_{1}^{2}}\]

C) \[\frac{{{n}_{2}}}{{{n}_{1}}}.\frac{{{r}_{1}}}{{{r}_{2}}}\]

D) \[\frac{{{n}_{1}}}{{{n}_{2}}}\]

Correct Answer: A

Solution :

[a] The mutual inductance of the inner coil

...(i)

Self inductance (L) of the inner coil is

...(ii)

Using (i) and (ii),