A small square loop of wire of side l is placed inside a large square loop of wire of side L(L l). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to (let I is the current passing through larger square loop)

Question

A small square loop of wire of side l is placed inside a large square loop of wire of side L(L > l). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to (let I is the current passing through larger square loop) (A) l / L (B) l2 / L (C) L / l (D) L2 / l

Tardigrade Admin · Accepted Answer

Magnetic field produced due to large loop

B = \frac{μ _{0}}{4 π} \frac{8 2 i}{L}

Flux linked with smaller loop

ϕ = B (l^{2}) = \frac{μ _{0}}{4 π} \frac{8 πi l ^{2}}{L}

∴ ϕ = M i

\Rightarrow M = \frac{ϕ}{i} = \frac{μ _{0}}{4 π} \cdot \frac{8 2 l l ^{2}}{L}

\Rightarrow M \propto \frac{l ^{2}}{L}

Q. A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L (L > l)$ . The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to (let $I$ is the current passing through larger square loop)

$l / L$

$l^{2} / L$

$L / l$

$L^{2} / l$

Q. A small square loop of wire of side l is placed inside a large square loop of wire of side L(L>l). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to (let I is the current passing through larger square loop)

l/L

l2/L

L/l

L2/l

Magnetic field produced due to large loop B=4πμ0​​L82​i​ Flux linked with smaller loop ϕ=B(l2)=4πμ0​​L8πil2​ ∴ϕ=Mi ⇒M=iϕ​=4πμ0​​⋅L82l​l2​ ⇒M∝Ll2​

Q. A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L (L > l)$ . The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to (let $I$ is the current passing through larger square loop)

$l / L$

$l^{2} / L$

$L / l$

$L^{2} / l$