Question 313: Magnetism and Matter

Question

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 V
0
. The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is 1 : $$\sqrt y $$ where y is ................. .

Accepted Answer

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]
$$ = {{8 	imes {{\sqrt 3 } \over 4} 	imes {a^2}} \over {6 	imes {a^2}}}$$
$${{{M_t}} \over {{M_s}}} = {1 \over {\sqrt 3 }}$$
y = 3

Magnetism and Matter

Integer / Numeric Answer Type