Question

a small square loop of wire of side 1mm is placed inside a large square loop of wire of side 10m the loops are coplanar and their centres coincide find the mutual inductance of the system

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student-name Arundhathy Pradeep asked in Physics

A small square loop of wire of side l is placed inside a large square loop of side L. The loops are coplanar and their centres coincide. The mutul inductance of the system is proportional to (a) l /L. (b) l^2/L

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student-name Sayantan Chakraborty answered this

842 helpful votes in Physics, Class XII-Science

Dear Student,

Magnetic Field at the centre of outer square current(I) carrying loop is

B1=22√μ0IπL

Since L>>l we approximate the magnetic field through entire inner coil by B1

Thus the flux through inner coil

φ21=B1A2=(22√μ0Iπ)×l2L

Mutual Inductance = φ21I1

or, M= (22√μ0π)×l2Lor, M= const×l2Lor, M∝l2L

Regards @sushantsingh