Verified Solution • 2025–26 Session moderate

QJEEM21Ph1570: JEE Main 2021 Physics - Class 12 JEEM21Ph1570 Solution: A uniform conducting wire of length is 24a, and resistance R is …

A uniform conducting wire of length is 24a, and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and then in the form of a square of side 'a'. The coil is connected to a voltage source V0. The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is 1 : y\sqrt y where y is ................. .

Step-by-Step Verified Solution

In triangle shape Nt=24a3a=8{N_t} = {{24a} \over {3a}} = 8

In square Ns=24a4a=6{N_s} = {{24a} \over {4a}} = 6

MtM3=NtIAtNsIAs{{{M_t}} \over {{M_3}}} = {{{N_t}I{A_t}} \over {{N_s}I{A_s}}} [I will be same in both]

=8×34×a26×a2= {{8 \times {{\sqrt 3 } \over 4} \times {a^2}} \over {6 \times {a^2}}}

MtMs=13{{{M_t}} \over {{M_s}}} = {1 \over {\sqrt 3 }}

y = 3

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