Physics · Magnetic field due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis, torque on a magnetic dipole in a uniform magnetic field
A short bar Magnet with its north pole facing North forms a neutral point P in t
A short bar Magnet with its north pole facing North forms a neutral point P in the horizontal plane. If the magnet is rotated by \( 90^{0} \) in the horizontal plane, the net magnetic induction at \( \mathrm{P} \) is: (Horizontal component of earths magnetic field is \( B_{H} \) )
- A. 0
- B. \( 2 B_{H} \)
- C. \( \frac{\sqrt{5}}{2} B_{H} \)
- D. \( \sqrt{5} B_{H} \)
Step-by-step solution
Initially, with north pole facing north, the neutral point P lies on the equatorial line of the magnet, where the magnet's field equals B_H in the opposite direction. After rotating the magnet by 90° in the horizontal plane, P lies on the axial line of the new orientation. The axial field is twice the equatorial field, so the magnet's field at P becomes 2B_H perpendicular to Earth's field. The net magnetic induction is the vector sum, with magnitude √((2B_H)^2 + B_H^2) = √5 B_H.
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