JEE MAIN - Physics (2021 - 27th August Morning Shift - No. 21)
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 : $$\sqrt y $$ where y is ................. .
Answer
3
Explanation
In triangle shape $${N_t} = {{24a} \over {3a}} = 8$$
In square $${N_s} = {{24a} \over {4a}} = 6$$
$${{{M_t}} \over {{M_3}}} = {{{N_t}I{A_t}} \over {{N_s}I{A_s}}}$$ [I will be same in both]
$$ = {{8 \times {{\sqrt 3 } \over 4} \times {a^2}} \over {6 \times {a^2}}}$$
$${{{M_t}} \over {{M_s}}} = {1 \over {\sqrt 3 }}$$
y = 3
In square $${N_s} = {{24a} \over {4a}} = 6$$
$${{{M_t}} \over {{M_3}}} = {{{N_t}I{A_t}} \over {{N_s}I{A_s}}}$$ [I will be same in both]
$$ = {{8 \times {{\sqrt 3 } \over 4} \times {a^2}} \over {6 \times {a^2}}}$$
$${{{M_t}} \over {{M_s}}} = {1 \over {\sqrt 3 }}$$
y = 3
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