CBSE Class 12-science Answered

Since the magnetic dipole comes to equilibrium, the torques due to both the magnetic field must cancel each other.

The three vectors, magnetic dipole, and the two magnetic fields must be coplanar.

Because, if they are not, the resultant of two magnetic fields will always be at a finite angle with the magnetic moment, and torque would not be zero.

τ₁ = τ₂

μB₁sinθ₁ = μB₂sinθ₂ 

B₁sin (60-15) = 1.2x10^-2xsin 15

B₁sin 45 = 1.2x10^-2xsin 15

B₁sin 45 = 1.2x10^-2xsin (60 - 45)

B₁sin 45 = 1.2x10^-2x(sin60 cos45 - cos60sin45)

B₁ = 1.2x10^-2x(sin60 cot45 - cos60)

B₁ = 1.2x10^-2x(3/2 - 1/2)

B₁ = 1.2x10^-2x(3 - 1)/2

B₁ = 0.44x10^-2 T and makes an angle 45 with magnetic dipole

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