A magnetic dipole is under the influence of two orthogonal magnetic fields, B1=0.5 × 10-3 T and B2=0.866 × 10-3 T . If the dipole comes to stable equilibrium at an angle θ with respect to B2 field, then the value of θ is

Question

A magnetic dipole is under the influence of two orthogonal magnetic fields, B1=0.5 × 10-3 T and B2=0.866 × 10-3 T . If the dipole comes to stable equilibrium at an angle θ with respect to B2 field, then the value of θ is (A) 45° (B) 30° (C) 60° (D) 90°

Tardigrade Admin · Accepted Answer

From tangent law, we have, m B2 sin θ=m B1 sin (90°-θ) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/105540bca0efdf74de8d0fde61a8a7c4-.png" /> ⇒ tan θ =(B1/B2)=(0.5 × 10-3/0.866 × 10-3) =((1/2)/(√3)2)=(1/√3) tan θ= tan 30° ⇒ θ=30°

Q. A magnetic dipole is under the influence of two orthogonal magnetic fields, $B_{1} = 0.5 \times 1 0^{- 3} T$ and $B_{2} = 0.866 \times 1 0^{- 3} T .$ If the dipole comes to stable equilibrium at an angle $θ$ with respect to $B_{2}$ field, then the value of $θ$ is

$4 5^{\circ}$

$3 0^{\circ}$

$6 0^{\circ}$

$9 0^{\circ}$

From tangent law, we have,
$m B_{2} sin θ = m B_{1} sin (9 0^{\circ} - θ)$

$\Rightarrow tan θ = \frac{B _{1}}{B _{2}} = \frac{0.5 \times 1 0 ^{- 3}}{0.866 \times 1 0 ^{- 3}}$
$= \frac{\frac{1}{2}}{\frac{3}{2}} = \frac{1}{3}$
$tan θ = tan 3 0^{\circ}$
$\Rightarrow θ = 3 0^{\circ}$

Q. A magnetic dipole is under the influence of two orthogonal magnetic fields, B1​=0.5×10−3T and B2​=0.866×10−3T. If the dipole comes to stable equilibrium at an angle θ with respect to B2​ field, then the value of θ is

45∘

30∘

60∘

90∘