• # question_answer Two small balls each carrying a charge q and mass m are attached to the ends of a light rod of length d which is suspended from the ceiling by a thin tension free fiber as shown in the figure. There is a uniform magnetic B pointing straight down, in the cylindrical region of radius R around the fiber. The system is initially at rest. If the magnetic field is turned off, which of the following describes what happens to the system immediately?     A) It rotates with angular momentum $qB{{R}^{2}}$      B) It rotates with angular momentum $\frac{qB{{d}^{2}}}{4}$ C) It rotates with angular velocity $\frac{qB{{R}^{2}}}{m{{d}^{2}}}$ D) It rotates with angular velocity $\frac{qB}{2m}$

Correct Answer: A

Solution :

[a] $\pi {{R}^{2}}\frac{dB}{dt}=E2\pi \frac{d}{2}\Rightarrow E=\frac{{{R}^{2}}}{d}\frac{dB}{dt}$ $\int{\tau dt=}\int{2q\frac{{{R}^{2}}}{d}\frac{d}{2}\left( \frac{dB}{dt} \right)dt=qB{{R}^{2}}=\Delta L}$

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