Find the value of L if the particle emerges from the region of magnetic field with its final velocity at an angle $30^{o}$ to its intital velocity.

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Solution

Let the particle emerge out from region of magnetic field at point B.
The magnetic force provides the centripetal acceleration. Hence
$\frac{m v_{0}^{2}}{R} = q v_{0} B_{0}$
$⟹ R = \frac{m v_{0}}{q B_{0}}$
From figure,
$R s i n 30^{\circ} = L$
$⟹ L = \frac{m v_{0}}{2 B_{0} q}$

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Find the value of L if the particle emerges from the region of magnetic field with its final velocity at an angle 30o to its intital velocity.

Let the particle emerge out from region of magnetic field at point B.The magnetic force provides the centripetal acceleration. Hencemv20R=qv0B0⟹R=mv0qB0From figure, Rsin30∘=L⟹L=mv02B0q

Find the value of L if the particle emerges from the region of magnetic field with its final velocity at an angle $30^{o}$ to its intital velocity.

Let the particle emerge out from region of magnetic field at point B.
The magnetic force provides the centripetal acceleration. Hence
$\frac{m v_{0}^{2}}{R} = q v_{0} B_{0}$
$⟹ R = \frac{m v_{0}}{q B_{0}}$
From figure,
$R s i n 30^{\circ} = L$
$⟹ L = \frac{m v_{0}}{2 B_{0} q}$