Home › UP Board Class 12 › Magnetism & EMI › The self-inductance of a long air-cored solenoid…
The self-inductance of a long air-cored solenoid of length $\ell$, cross-sectional area $A$ and total number of turns $N$ is:
A$\mu_0 N A \ell$
B$\mu_0 N^2 A \ell$
C$\mu_0 N^2 A / \ell$
D$\mu_0 N A / \ell$
Answer & Solution
Correct answer: C. $\mu_0 N^2 A / \ell$
For a long solenoid the field inside is $B = \mu_0 n I = \mu_0 (N/\ell) I$. Flux through each turn is $BA$ and total linkage is $N(BA)$, giving $L = N\Phi/I = \mu_0 N^2 A / \ell$. Equivalently $L = \mu_0 n^2 A \ell$ if $n = N/\ell$.
Related questions
A storage battery of emf 8.0 V and internal resistance 0.5 $\Omega$ is charged by a 120 V The number density of free electrons in a copper wire is $8.5 \times 10^{28}\ \text{m}^{-3A heating element has resistance 100 $\Omega$ at 27.0 °C. Its temperature coefficient of rA wire of length 15 m and uniform cross-section $6.0 \times 10^{-7}\ \text{m}^2$ has a meaThe statement "$V = IR$ is itself the statement of Ohm's law" is, according to the text, iCurrent through an area of cross-section is treated as a scalar quantity in this chapter eA Wheatstone bridge has arms AB = 100 $\Omega$, BC = 10 $\Omega$, CD = 5 $\Omega$, DA = 60In a Wheatstone bridge the unknown resistance is placed in the fourth arm. Known resistanc