An electron revolves around the nucleus in a circular path with angular momentum $L$. A uniform magnetic field $B$ is applied perpendicular to the plane of its orbit. If the electron experiences a torque $T$, then
- T || L
- T is anti- parallel to L
- T . L=0
- Angle between T and L is 45°
The Correct Option is C
Solution and Explanation
Given: - An electron revolves in a circular orbit with angular momentum \( \vec{L} \) - A uniform magnetic field \( \vec{B} \) is applied perpendicular to the plane of the orbit - Electron experiences a torque \( \vec{T} \)
Concept: A magnetic moment \( \vec{\mu} \) associated with the electron is given by: \[ \vec{\mu} \propto \vec{L} \] When placed in a magnetic field, the torque experienced is: \[ \vec{T} = \vec{\mu} \times \vec{B} \] Since \( \vec{T} \) is the cross product of \( \vec{\mu} \) and \( \vec{B} \), and \( \vec{L} \) is in the direction of \( \vec{\mu} \), we get: \[ \vec{T} \cdot \vec{L} = 0 \] because the torque is perpendicular to the angular momentum vector.
Final Answer: \( \vec{T} \cdot \vec{L} = 0 \)
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