A current I flows in a rectangularly shaped wire whose center lies at (x0, 0,0) and whose vertices are located at the points A(x0 + d, - a, -b), B(x0 - d, a, -b), C(x0 - d, a, b), and D(x0 + d, -a, b) respectively. Assume that a,b, d

Question

A current I flows in a rectangularly shaped wire whose center lies at (x0, 0,0) and whose vertices are located at the points A(x0 + d, - a, -b), B(x0 - d, a, -b), C(x0 - d, a, b), and D(x0 + d, -a, b) respectively. Assume that a,b, d < < x0 Find the magnitude of magnetic dipole moment vector of the rectangular wire frame. (Given: b = 10 m, d = 4 m, a = 3 m, I= 0.01 A) (A) 2 J T-1 (B) 4 J T-1 (C) 3 J T-1 (D) 9 J T-1

Tardigrade Admin · Accepted Answer

Magnetic moment of a current carrying loop,

μ = I S

Area of the loop,

S = A B \times BC

Here,

A B = - 2 d \hat{i} + 2 a \hat{j}, BC = 2 b \hat{k}

∴ S = (- 2 d \hat{i} + 2 a \hat{j}) \times (2 b \hat{k})

= 4 b d \hat{j} + 4 ab \hat{i}

∴ ∣ μ ∣ = I ∣ ∣ S ∣ ∣ = 4 I b a^{2} + d^{2}

= 4 \times 0.01 \times 10 \times 3^{2} + 4^{2}

= 0.4 \times 5 = 2 J T^{- 1}

$2 J T^{- 1}$

$4 J T^{- 1}$

$3 J T^{- 1}$

$9 J T^{- 1}$

2JT−1

4JT−1

3JT−1

9JT−1

Magnetic moment of a current carrying loop, μ​=IS Area of the loop, S=AB×BC Here, AB=−2di^+2aj^​,BC=2bk^ ∴S=(−2di^+2aj^​)×(2bk^) =4bdj^​+4abi^ ∴∣μ​∣=I∣∣​S∣∣​=4Iba2+d2​ =4×0.01×10×32+42​ =0.4×5=2JT−1

$2 J T^{- 1}$

$4 J T^{- 1}$

$3 J T^{- 1}$

$9 J T^{- 1}$