A uniform conducting wire of length and resistance is wound up as a current carrying coil in the shape of (i) an equilateral triangle of side (ii) a square of side The magnetic dipole moment of the coil in each case respectively are

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Q.
A uniform conducting wire of length $12 a$ and resistance $' R'$ is wound up as a current carrying coil in the shape of

(i) an equilateral triangle of side $' a' .$

(ii) a square of side $' a' .$

The magnetic dipole moment of the coil in each case respectively are [2021]

1 $4 I a^{2}$ and $3 I a^{2}$

2 $\sqrt{3} I a^{2}$ and $3 I a^{2}$

3 $3 I a^{2}$ and $I a^{2}$

4 $3 I a^{2}$ and $4 I a^{2}$

Ans.
(2)

For an equilateral triangle of side $a$ :

As total length of the wire $= 12 a$

So, number of loops, $n = \frac{12 a}{3 a} = 4$

Magnetic moment of coil, $M = n I A$ ...(i)

Area of triangle, $A = \frac{\sqrt{3}}{4} a^{2}$

From equation (i), $M = 4 I \frac{\sqrt{3}}{4} a^{2} ∴ M = \sqrt{3} I a^{2}$

For a square of side $a :$ Area, $A = a^{2}$

Number of loops, $n = \frac{12 a}{4 a} = 3$

Magnetic moment, $M = n I A = 3 I (a^{2}) = 3 I a^{2}$

Solution

Q.
A uniform conducting wire of length $12 a$ and resistance $' R'$ is wound up as a current carrying coil in the shape of

(i) an equilateral triangle of side $' a' .$

(ii) a square of side $' a' .$

The magnetic dipole moment of the coil in each case respectively are [2021]

1 $4 I a^{2}$ and $3 I a^{2}$

2 $\sqrt{3} I a^{2}$ and $3 I a^{2}$

3 $3 I a^{2}$ and $I a^{2}$

4 $3 I a^{2}$ and $4 I a^{2}$

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Solution

Q. A uniform conducting wire of length 12a and resistance 'R' is wound up as a current carrying coil in the shape of (i) an equilateral triangle of side 'a'. (ii) a square of side 'a'. The magnetic dipole moment of the coil in each case respectively are [2021]

1 4Ia2 and 3Ia2

2 3Ia2 and 3Ia2

3 3Ia2 and Ia2

4 3Ia2 and 4Ia2

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Q.
A uniform conducting wire of length $12 a$ and resistance $' R'$ is wound up as a current carrying coil in the shape of

(i) an equilateral triangle of side $' a' .$

(ii) a square of side $' a' .$

The magnetic dipole moment of the coil in each case respectively are [2021]

1 $4 I a^{2}$ and $3 I a^{2}$

2 $\sqrt{3} I a^{2}$ and $3 I a^{2}$

3 $3 I a^{2}$ and $I a^{2}$

4 $3 I a^{2}$ and $4 I a^{2}$