JEE Main 27 Aug 2021 Shift 1 Solved Paper

Length of conducting wire, l = 24 a Resistance of wire is R. Ratio of magnetic moment of coil for equilateral triangle to square is $1: \sqrt{y}$. Side of equilateral triangle is a and also side of square is a. Number of turns in equilateral triangle will be $n_{T}=\frac{24 a}{3 a}=8$ [ ∵ Length of one turn is 3a] Number of turns in square will be $n_{S}=\frac{24 a}{4 a}=6$ [ ∵ 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 $\frac{M_{T}}{M_{S}}=\frac{n_{T} IA_{T}}{n_{S} IA_{S}}$ (∵ I is same in both coils) Substituting the values in above expression, we get $\frac{1}{\sqrt{y}}=\frac{8 \times \frac{\sqrt{3}}{4} a^{2}}{6 \times a^{2}}=\frac{8 \sqrt{3}}{24}=\frac{1}{\sqrt{3}}$ $\Rightarrow \sqrt{y}=\sqrt{3}$ ⇒ y = 3 Hence, the value of y is 3.