JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Magnetic Effects of Current

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A uniform conducting wire of length is 24 a, 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 : y

where

y

is ______

Answer: 3

Solution

For equilateral triangle: perimeter =

3 a

, so wire makes

\frac{24 a}{3 a} = 8

turns. Area =

\frac{3}{4} a^{2}

. Magnetic moment

M_{T} = n I A = 8 \times I \times \frac{3}{4} a^{2} = 23 I a^{2}

.

For square: perimeter =

4 a

, so wire makes

\frac{24 a}{4 a} = 6

turns. Area =

a^{2}

. Magnetic moment

M_{S} = 6 \times I \times a^{2} = 6 I a^{2}

.

Ratio:

\frac{M _{T}}{M _{S}} = \frac{2 3 I a ^{2}}{6 I a ^{2}} = \frac{3}{3} = \frac{1}{3}

. Therefore

y = 3

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Integer answer

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JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Magnetic Effects of Current

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