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 fiber as shown in figure. There is a uniform magnetic field 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 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 $\frac { \mathrm { qBR } ^ { 2 } } { 2 }$
• D. None of the above**[C]**

Answer 1

Answer: (C)

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

Answer 2

=

πR² $\frac { \mathrm { dB } } { \mathrm { dt } }$ = E × 2πd

E = $\frac { \mathrm { dB } } { \mathrm { dt } }$ =

Change in angular momentum of whole system

= τ × ∆t × 2

= qE × $\frac { \mathrm { qBR } ^ { 2 } } { 2 }$