Question

Two concentric circular coils, one of small radius r1 having N1 turns and the other of large radius r2 having N2 turns such that r1 <

Answer 1

Solution:

$\sf\red{N_1 = no. \: of \: turns \: per \: unit \: length \: of \: inner \: coil}$

$\sf\red{N_2 = no. \: of \: turns \: per \: unit \: length \: of \: outer \: coil} </p><p>\sf\red{r_1 and r_2 radius}$

$\sf\red{L= length of coil (both)}</p><p></p><p>\sf\red{L_1 = current flowing in inner coil}$

$\sf\red{Magnetic field B due to this current}</p><p>\sf\red{Bis only inside coil 1 }</p><p>\sf\red{Outside coil IB=0}</p><p>\sf\red{Magnetic flux through I turn of coil 2 due to B is}$

$\sf\red{ϕ=B × Area = μ_0n_1i_1 × z^r_2}$

$\sf\red{Total no. of turns in coil 2=n_2 × L}\\</p><p></p><p>\sf\red{Mutual inductance M is ϕ = M × i}\\</p><p></p><p>\sf\red{So, M=μ_0n_1n_2zr^2L}$