Question

Two small pith balls, each carrying a charge q are attached to the ends of a light rod of length d, which is suspended from the ceiling by a thin torsion free fibre as shown in figure. There is a uniform magnetic field B pointing straight down, in the cylindrical region of radius R around the fibre. The system is initially at rest. If the magnetic field is turned off, which of the following happen to the system –

• A. It rotate with an angular momentum qBR²
• B. It does not move at all
• C. It rotate with an angular momentum $\frac{qBR^{2}}{2}$
• D. None of the above

Answer 1

Answer: (C)

It rotate with an angular momentum $\frac{qBR^{2}}{2}$

Answer 2

$\frac{d\varphi}{dt} = \int_{}^{}{E.dl}$

p R² $\frac{dB}{dt}$ = E× 2pd

E = $\frac{R^{2}}{2d}\frac{dB}{dt} = \frac{R^{2}}{2d}\frac{B}{\Delta t}$

Change in angular momentum of whole system

= τ × Dt × 2

= qE ×$\frac{d}{2}$ × Dt × 2 = $\frac{qBR^{2}}{2}$