A long solenoid has self inductance L. If its length is doubled keeping total number of turns constant then its new self inductance will be

Question

A long solenoid has self inductance L. If its length is doubled keeping total number of turns constant then its new self inductance will be (A) (L/2) (B) 2 L (C) L (D) (L/4)

Tardigrade Admin · Accepted Answer

L=μ0 n2 A l L=μ0((N/I))2 A l L=(μ0 N2/l) A ⇒ L propto (1/l) ⇒ L'=(L/2)

Q. A long solenoid has self inductance $L$ . If its length is doubled keeping total number of turns constant then its new self inductance will be

$\frac{L}{2}$

$2 L$

$L$

$\frac{L}{4}$

$L = μ_{0} n^{2} A l$
$L = μ_{0} (\frac{N}{I})^{2} A l$
$L = \frac{μ _{0} N ^{2}}{l} A$
$\Rightarrow L \propto \frac{1}{l}$
$\Rightarrow L^{'} = \frac{L}{2}$

Q. A long solenoid has self inductance L. If its length is doubled keeping total number of turns constant then its new self inductance will be

2L​

2L

L

4L​

L=μ0​n2Al L=μ0​(IN​)2Al L=lμ0​N2​A ⇒L∝l1​ ⇒L′=2L​

Q. A long solenoid has self inductance $L$ . If its length is doubled keeping total number of turns constant then its new self inductance will be

$\frac{L}{2}$

$2 L$

$L$

$\frac{L}{4}$

$L = μ_{0} n^{2} A l$
$L = μ_{0} (\frac{N}{I})^{2} A l$
$L = \frac{μ _{0} N ^{2}}{l} A$
$\Rightarrow L \propto \frac{1}{l}$
$\Rightarrow L^{'} = \frac{L}{2}$