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JEE Main 2026 · 4 Apr · Shift 2, Physics question 48

Two identical small bar magnets each of dipole moment 353\sqrt5 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 α×10−3\alpha\times10^{-3} T. The value of α\alpha is ________.
(μ0=4π×10−7\mu_0=4\pi\times10^{-7} Tm/A)

Left: a bar magnet lying horizontally (S on the left, N on the right). Right, 10 cm away centre to centre: a bar magnet standing vertically (S on top, N below). P lies midway on the dashed line joining their centres, i.e. on the axis of the left magnet and on the equatorial line of the right one.
Answer and worked solution

Official answer: 12

Position of P. P is 5 cm from each magnet: on the axis of the left one and on the equator of the right one.

Fields.

  • Axial: B1=10−7⋅2(35)(0.05)3=4.85×10−3B_1=10^{-7}\cdot\dfrac{2(3\sqrt5)}{(0.05)^3}=4.8\sqrt5\times10^{-3} T.
  • Equatorial: B2=2.45×10−3B_2=2.4\sqrt5\times10^{-3} T.

Resultant. They are perpendicular: B=5×10−34.82+2.42=5⋅2.45×10−3=12×10−3B=\sqrt5\times10^{-3}\sqrt{4.8^2+2.4^2}=\sqrt5\cdot2.4\sqrt5\times10^{-3}=12\times10^{-3} T.

Answer: 12

Topics:Magnetic dipole and bar magnet
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