Q. What is the self inductance of a solenoid of length 31.4 cm, area of cross-section $10^{- 3}m^{2}$ and total number of turns $10^{3}?$
A) 4 mH
B) 4 H
C) 40 H
D) 0.4 H
Explanation
(a) $A = 10^{- 3}m^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ l = 31.4 = 31.4 \times 10^{- 2}m$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ n = 10^{- 3}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \phi = Li$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ BA = Li$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mu_{0}NiA = Li$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ L = \mu_{0}nlA$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 4\pi \times 10^{- 7} \times 10^{3} \times 31.4 \times 10^{- 2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 4mH$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.