Comprehension A uniform and transverse magnetic field exists into a regular hexagonal region as ...

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Comprehension
A uniform and transverse magnetic field exists into a regular hexagonal region as shown in figure. A charged particle \( q \) is thrown into the magnetic field with speed along line \( O A \)

Find the displacement and average velocity during the time it remains in magnetic field
(a) \( a \sqrt{3}, \frac{q B a}{\pi m} \)
(b) \( a \sqrt{3}, 3 \sqrt{3} \frac{q B a}{\pi m} \)
(c) \( \frac{a}{\sqrt{3}}, \frac{q B a}{\pi m} \)
(d) \( \frac{a}{\sqrt{3}}, \frac{3 \sqrt{3} q B a}{\pi m} \)
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