Question

A coil is wound on a frame of rectangular cross-section. If all the linear dimensions of the frame are increased by a factor $2$ and the number of turns per unit of the coil remains the same, self-inductance of the coil increases by a factor of :

• A. $4$
• B. $8$
• C. $12$
• D. $16$

Answer 1

The correct option is B $8$

Self inductance $={\mu }_0{n}^{2}AL={\mu }_0{n}^2(l\times b)\times L$
$n=$ Total number of turns /length
$L=$ Length of inductor
$l=$ Length of rectangular cross section
$b=$ breadth of rectangular cross-section
So, when all linear dimensions are increased by a factor of 2.
The new self inductance becomes $L^{\prime }=8L$.