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Four identical charged particles each of mass 0.1kg and charge 2C connected to other via mass less non – conducting rods of equal length. The whole arrangement is placed, in cylindrical region carrying a uniform magnetic field as shown in figure $(B_{0} = 4 T, a = 1 m)$ . Suddenly the magnetic field is switched off. Choose the correct statement(s)

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The angular momentum of the system is

8 \sqrt{2} N m / s

Angular velocity of the system is 40 rad/s

The angular momentum of the system is 8 Nm/s

The magnetic field at point O immediately after the magnetic field is switched off is non zero

answer is A, C, D.

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Detailed Solution

According to Newton’s second law of motion

$τ = \frac{d L}{d t} o r \int_{0}^{t} τ d t = L_{f} - L_{i} \Rightarrow \int_{}^{} 4 q E \frac{a}{\sqrt{2}} d t = L_{f}$

$q a^{2} B_{0} = 2 m a^{2} ω, ω = \frac{q B_{0}}{2 m}$

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