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Derive the equation of torque on a magnetic needle in a uniform magnetic field. |
Answer» Solution :A compass needle of magnetic moment m is placed in a uniform magnetic field as shown in figure.  `NS=` magnetic length `=2l` `q_m=` strength of each POLE Magnetic dipole moment `m= q_(m) (2l)` ACCORDING to figure in right ANGLE `THETA NDS`, `ND=2 l sin theta` Force on S pole `=F_S = - q_m` B Force on N pole `=F_N = q_m B` These equal and unlike forces form a couple which tend to rotate the needle clockwise. {The torque on the needle} = {magnitude of either force `xx` perpendicular distance between the two forces.} `tau = q_m B xx ND` `tau = q_m B xx 2l sin theta` `tau = q_m (2l) B sin theta ` `THEREFORE tau = m B sin theta ` where `q_m (2l) =` magnetic dipole moment `m` `therefore overset(to) (tau) = overset(to) (m) xx overset(to) (B) ( because m and B` are vectors `)` |
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