A) \[L\propto R\]
B) \[L\propto 1/R\]
C) \[L\propto {{R}^{2}}\]
D) \[L\propto {{R}^{3}}\]
Correct Answer: C
Solution :
The inductance of a solenoid is \[L={{\mu }_{0}}{{n}^{2}}\,Al\] where A is the area of cross-section of the solenoid, l its length and n is the number of turns per unit length As \[A=\pi {{R}^{2}}\], where R is the radius of the solenoid \[\therefore \,\,\,\,L={{\mu }_{0}}{{n}^{2}}\pi {{R}^{2}}l\Rightarrow L\propto {{R}^{2}}\]
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