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Protons move rectilinearly in the region of space where there are uniform mutually perpendicular electric and magnetic field E and B. The trajectory of protons lies in the plane xz as shown in the figure and forms an angle $θ$ such x-axis. Find the pitch of the helical trajectory along which the protons still move after the electric field is switched off.
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$\frac{2 πmEtanθ}{q B^{2}}$

$\frac{4 πmEtanθ}{q B^{2}}$

$\frac{2 πEtanθ}{q B^{2}}$

$\frac{πmEtanθ}{q B^{2}}$

answer is C.

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Detailed Solution

When they are moving rectilinearly, net force is zero.

$∴ q E = B q v \sin (90 °) ∴ v = \frac{E}{B \cos θ}$

When electric field is switched off,

$p = (\frac{2 πm}{B q}) v \cos (90 ° - θ) = \frac{2 πm E tanθ}{q B^{2}}$

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