Two magnets A and B are identical and these are arranged as shown in the figure. Their length is negligible in comparison to the separation between them. A magnetic needle is placed between the magnets at point P which gets deflected through an angle θ under the influence of magnets. The ratio of distance d1 and d2 will be

Question

Two magnets A and B are identical and these are arranged as shown in the figure. Their length is negligible in comparison to the separation between them. A magnetic needle is placed between the magnets at point P which gets deflected through an angle θ under the influence of magnets. The ratio of distance d1 and d2 will be (A) (2 tan θ)1 / 3 (B) (2 tan θ)-1 / 3 (C) (2 cot θ)1 / 3 (D) (2 cot θ)-1 / 3

Tardigrade Admin · Accepted Answer

In equilibrium, B1=B2 tan θ <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/dc4ed49ea9900e7af6fdc84599a983e3-.png" /> ⇒ (μ0/4 π) ⋅ (2 M/d13)=(μ0/4 π) ⋅ (M/d23) tan θ ⇒ (d1/d2)=(2 cot θ)1 / 3

$(2 tan θ)^{1/3}$

$(2 tan θ)^{- 1/3}$

$(2 cot θ)^{1/3}$

$(2 cot θ)^{- 1/3}$

In equilibrium, $B_{1} = B_{2} tan θ$

$\Rightarrow \frac{μ _{0}}{4 π} \cdot \frac{2 M}{d _{1}^{3}} = \frac{μ _{0}}{4 π} \cdot \frac{M}{d _{2}^{3}} tan θ$
$\Rightarrow \frac{d _{1}}{d _{2}} = (2 cot θ)^{1/3}$

(2tanθ)1/3

(2tanθ)−1/3

(2cotθ)1/3

(2cotθ)−1/3

In equilibrium, B1​=B2​tanθ ⇒4πμ0​​⋅d13​2M​=4πμ0​​⋅d23​M​tanθ ⇒d2​d1​​=(2cotθ)1/3

$(2 tan θ)^{1/3}$

$(2 tan θ)^{- 1/3}$

$(2 cot θ)^{1/3}$

$(2 cot θ)^{- 1/3}$

In equilibrium, $B_{1} = B_{2} tan θ$

$\Rightarrow \frac{μ _{0}}{4 π} \cdot \frac{2 M}{d _{1}^{3}} = \frac{μ _{0}}{4 π} \cdot \frac{M}{d _{2}^{3}} tan θ$
$\Rightarrow \frac{d _{1}}{d _{2}} = (2 cot θ)^{1/3}$