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 moments of the coil in each case respectively are:

Question

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 moments of the coil in each case respectively are: (A) √3 Ia 2 and 3 Ia 2 (B) 3 Ia 2 and Ia 2 (C) 3 Ia 2 and 4 Ia 2 (D) 4 Ia 2 and 3 Ia 2

Tardigrade Admin · Accepted Answer

(i) If it is an equilateral triangle of side '

a

' no. of triangular loops formed

\frac{12 a}{3 a} = 4

and magnetic moment

4 \cdot \frac{3 a ^{2}}{4} l = 3 l a^{2}

(ii) Side of the square if it is a.
No. of square formed

\frac{12 a}{4 a} = 3

Magnetic moment of the square loop is

3 a^{2} I

.

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 moments of the coil in each case respectively are:

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

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

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

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

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 moments of the coil in each case respectively are:

3​Ia2 and 3Ia2

3Ia2 and Ia2

3Ia2 and 4Ia2

4Ia2 and 3Ia2

(i) If it is an equilateral triangle of side 'a' no. of triangular loops formed 3a12a​=4 and magnetic moment 4⋅43​a2​l=3​la2 (ii) Side of the square if it is a. No. of square formed 4a12a​=3 Magnetic moment of the square loop is 3a2I.

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 moments of the coil in each case respectively are:

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

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

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

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