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Derive an expression for magnetic potential energy .for a magnetic dipole kept in a uniform magnetic field. |
Answer» Solution :As shown in FIGURE a bar magnet is held at an angle `theta` with the direction of a uniform magnetic field `overset(to) (B)`. The potential energy of this bar magnet is indicated by `U_(m)`, `U_(m) = int tau (theta) d theta` `= int m B sin theta d theta` `= - m B cos theta` `U= - overset(to) (m). overset(to)(B)...(1)` SPECIAL cases : (1) If bar magnet MAKES an angle `0^@` with magnetic field `overset(to) (B)`. U = - MB which is the minimum value of potential energy. The magnet is in most stable position. (2) If bar magnet makes an angle 180° with magnetic field `overset(to) (B)`. U = + mB which is the maximum value of potential energy. The magnet is in most unstable position. (3) If bar magnet is perpendicular to `overset(to)(B)`, `U= m B cos 90^@` `U=0` |
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