Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ' R ' is placed inside a large square loop of wire of side L (L gg R). The loops are coplanar and their centres coincide:

Question

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ' R ' is placed inside a large square loop of wire of side L (L gg R). The loops are coplanar and their centres coincide: (A) M=(2 √2 μ0 R2/L) (B) M=(√2 μ0 R2/L) (C) M=(2 √2 μ0 R/L2) (D) M=(√2 μ0 R/L2)

Tardigrade Admin · Accepted Answer

φ= Mi φ=( BA ) φ=π R 2(4 (μ0/4 π) ( i /(( L )2)) √2) ⇒ M =(2 √2 μ0 R 2/ L )

Q. Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ' $R$ ' is placed inside a large square loop of wire of side $L$ $(L ≫ R)$ . The loops are coplanar and their centres coincide:

$M = \frac{2 2 μ _{0} R ^{2}}{L}$

$M = \frac{2 μ _{0} R ^{2}}{L}$

$M = \frac{2 2 μ _{0} R}{L ^{2}}$

$M = \frac{2 μ _{0} R}{L ^{2}}$

$ϕ = M i$
$ϕ = (B A)$
$ϕ = π R^{2} (4 \frac{μ _{0}}{4 π} \frac{i}{( \frac{L}{2} )} 2)$
$\Rightarrow M = \frac{2 2 μ _{0} R ^{2}}{L}$

Q. Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ' R ' is placed inside a large square loop of wire of side L (L≫R). The loops are coplanar and their centres coincide:

M=L22​μ0​R2​

M=L2​μ0​R2​

M=L222​μ0​R​

M=L22​μ0​R​