A) \[L\propto R\]
B) \[L\propto l/R\]
C) \[L\propto {{R}^{2}}\]
D) \[L\propto {{R}^{3}}\]
Correct Answer: C
Solution :
(c) \[L\propto {{R}^{2}}\] 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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