A small square loop of wire of side l is placed inside a large square loop of side L(Ll). If the loops are coplanar and their centres coincide, the mutual induction of the system is directly proportional to :

Question

A small square loop of wire of side l is placed inside a large square loop of side L(L>>l). If the loops are coplanar and their centres coincide, the mutual induction of the system is directly proportional to : (A) (L/l) (B) (l/L) (C) (L2/l) (D) (l2/L)

Tardigrade Admin · Accepted Answer

Considering the larger loop to be made up of four rods each of length

L

, the field at the centre, i.e., at a distance

(\frac{L}{2})

from each rod,
will he

B = 4 \times \frac{μ _{0}}{4 π} \frac{l}{d} [sin α + sin β]

i.e.,

B = 4 \times \frac{μ _{0}}{4 π} \frac{I}{( \frac{L}{2} )} \times 2 sin 45

i.e.,

B_{1} = \frac{μ _{0}}{4 π} \frac{8 2}{L} I

So, the flux with smaller loop

ϕ_{2} = B_{1} S_{2} = \frac{μ _{0}}{4 π} \frac{8 2}{L} l^{2} I

and hence,

M = \frac{ϕ _{2}}{I} = 22 \frac{μ _{0}}{π} \frac{l ^{2}}{L}

or

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

Q. A small square loop of wire of side $l$ is placed inside a large square loop of side $L (L >> l)$ . If the loops are coplanar and their centres coincide, the mutual induction of the system is directly proportional to :

$\frac{L}{l}$

$\frac{l}{L}$

$\frac{L ^{2}}{l}$

$\frac{l ^{2}}{L}$

Q. A small square loop of wire of side l is placed inside a large square loop of side L(L>>l). If the loops are coplanar and their centres coincide, the mutual induction of the system is directly proportional to :

lL​

Ll​

lL2​

Ll2​

Q. A small square loop of wire of side $l$ is placed inside a large square loop of side $L (L >> l)$ . If the loops are coplanar and their centres coincide, the mutual induction of the system is directly proportional to :

$\frac{L}{l}$

$\frac{l}{L}$

$\frac{L ^{2}}{l}$

$\frac{l ^{2}}{L}$