There are two long co-axial solenoids of same length l. the inner and outer coils have radii r1 and r2 and number of turns per unit length n1 and n2 respectively. The rate of mutual inductance to the self-inductance of the inner-coil is :

Question

There are two long co-axial solenoids of same length l. the inner and outer coils have radii r1 and r2 and number of turns per unit length n1 and n2 respectively. The rate of mutual inductance to the self-inductance of the inner-coil is : (A) (n2/n1). (r22/r12)  (B) (n2/n1). (r1/r2)  (C) (n1/n2) (D) (n2/n1)

Tardigrade Admin · Accepted Answer

M = μ0 n1n2 π r21 L =μ0 n12 π r21 ⇒ (M/L) = (n2/n1)

Q. There are two long co-axial solenoids of same length $l$ . the inner and outer coils have radii $r_{1}$ and $r_{2}$ and number of turns per unit length $n_{1}$ and $n_{2}$ respectively. The rate of mutual inductance to the self-inductance of the inner-coil is :

$\frac{n _{2}}{n _{1}} . \frac{r _{2}^{2}}{r _{1}^{2}}$

$\frac{n _{2}}{n _{1}} . \frac{r _{1}}{r _{2}}$

$\frac{n _{1}}{n _{2}}$

$\frac{n _{2}}{n _{1}}$

$M = μ_{0} n_{1} n_{2} π r_{1}^{2}$
$L = μ_{0} n_{1}^{2} π r_{1}^{2}$
$\Rightarrow \frac{M}{L} = \frac{n _{2}}{n _{1}}$

Q. There are two long co-axial solenoids of same length l. the inner and outer coils have radii r1​ and r2​ and number of turns per unit length n1​ and n2​ respectively. The rate of mutual inductance to the self-inductance of the inner-coil is :

n1​n2​​.r12​r22​​

n1​n2​​.r2​r1​​

n2​n1​​

n1​n2​​