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Concepts Of Physics MCQ Edition [Volume 2]PhysicsPermanent Magnets

A magnetic dipole having a magnetic moment of 0.72 2 A m ^2 is oriented horizontally such that its north pole points towards the east. Determine the position of a neutral point, given that the horizontal component of the earth's magnetic field is 18 T .

Options

  1. A20 cm from the dipole, ⁻¹( 2 ) south of east
  2. B20 cm from the dipole, ⁻¹( 2 ) north of east
  3. C20 cm from the dipole, ⁻¹ ( 1 2 ) south of east
  4. D40 cm from the dipole, ⁻¹( 2 ) south of east

Correct answer

A. 20 cm from the dipole, ⁻¹( 2 ) south of east

Step-by-step solution

Let the east direction be along the positive x-axis ( i ) and the north direction be along the positive y-axis ( j ). The magnetic moment of the dipole is M = M i , where M = 0.72 2 A m ^2 . The horizontal component of the earth's magnetic field is B _H = B_H j , where B_H = 18 T = 18 10⁻⁶ T . At the neutral point, the magnetic field due to the dipole B _d must exactly cancel the earth's magnetic field, so B _d = -B_H j . The magnetic field of a dipole at a position vector r is given by: B _d = ₀ 4 r^3 [3( M r ) r

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