Question

in the figure theta=tan-1(√2) the correct direction of magnetic field​

Answer 1

Thus the correct direction of the magnetic field is θ = tan⁻¹ √ 2

Explanation:

For M.cosθ pt P is at axis, so direction of magnetic field will be along M.cosθ and for M.sinθ pt P is perpendicular

So, direction will be just opposite to M Sinθ

Bₐ = (μ₀/ 4π) × (2M cosθ)/r³

B₁ = (μ₀/ 4π) × (2M sinθ)/r³

tanα = B₁/Bₐ = (tanθ)/2

Given that:

θ = tan⁻¹ / √ 2

or tanθ = √ 2 /2 = 1/2

tanα = 1/ tanθ

tanα = cotθ

tanα = tan(π/2 - θ)

θ = (π/2 - θ)

or θ + θ = π/2

Thus the correct direction of the magnetic field is θ = tan⁻¹ √ 2

Answer 2

The correct direction of the magnetic field is tan⁻¹ √2

Given:

θ = tan⁻¹/√2

Explanation:

The image given in the question is attached below.

For M cosθ pt P is at axis, so direction of magnetic field will be along M cosθ and for M sinθ pt P is perpendicular

So, direction will be just opposite to M sinθ

Bₐ = ((μ₀/ 4π) × (2M cosθ))/r³

B₁ = ((μ₀/ 4π) × (2M sinθ))/r³

tanα = B₁/Bₐ = (tanθ)/2

From given,

tanθ = √2/2 = 1/2

tanα = 1/tanθ

tanα = cotθ

tanα = tan(π/2 - θ)

θ = (π/2 - θ)

θ + θ = π/2

∴ θ = tan⁻¹ √2