Two identical small bar magnets each of dipole moment 3 5 J/T are placed at a center to center separation of 10 cm, with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point P midway between the magnets is 10⁻³ T. The value of is ______. ( ₀=4 10⁻⁷ Tm/A)

Step-by-step solution

Let the magnetic moment of each magnet be M = 3 5 J/T. The distance of point P from the center of each magnet is r = 5 cm = 0.05 m. For the first magnet (horizontal), point P lies on its axial line. The magnetic field at P due to the first magnet is: B₁ = ₀ 4 2M r^3 The direction of B ₁ is along the axis of the first magnet. For the second magnet (vertical), point P lies on its equatorial line. The magnetic field at P due to the second magnet is: B₂ = ₀ 4 M r^3 The direction of B ₂ is parallel to the axis of the se