| 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? |
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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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