Torque

Given: - An electron revolves in a circular orbit with angular momentum $%5Cvec%7BL%7D$ - A uniform magnetic field $%5Cvec%7BB%7D$ is applied perpendicular to the plane of the orbit - Electron experiences a torque $%5Cvec%7BT%7D$

Concept: A magnetic moment $%5Cvec%7B%5Cmu%7D$ associated with the electron is given by: $%5Cvec%7B%5Cmu%7D%20%5Cpropto%20%5Cvec%7BL%7D$ When placed in a magnetic field, the torque experienced is: $%5Cvec%7BT%7D%20%3D%20%5Cvec%7B%5Cmu%7D%20%5Ctimes%20%5Cvec%7BB%7D$ Since $%5Cvec%7BT%7D$ is the cross product of $%5Cvec%7B%5Cmu%7D$ and $%5Cvec%7BB%7D$ , and $%5Cvec%7BL%7D$ is in the direction of $%5Cvec%7B%5Cmu%7D$ , we get: $%5Cvec%7BT%7D%20%5Ccdot%20%5Cvec%7BL%7D%20%3D%200$ because the torque is perpendicular to the angular momentum vector.

Final Answer: $%5Cvec%7BT%7D%20%5Ccdot%20%5Cvec%7BL%7D%20%3D%200$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Torque

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs