Length of conducting wire, l = 24 a
Resistance of wire is R.
Ratio of magnetic moment of coil for equilateral triangle to square is
1:√y.
Side of equilateral triangle is a and also side of square is a.
Number of turns in equilateral triangle will be
nT==8 [ ∵ Length of one turn is 3a]
Number of turns in square will be
nS==6 [ ∵ Length of one turn is 4a]
Magnetic moment of coil is given as
M = nIA
The ratio of magnetic moment for triangular coil to square coil is given as
= (∵ I is same in both coils)
Substituting the values in above expression, we get
=== ⇒√y=√3 ⇒ y = 3
Hence, the value of y is 3.