A uniform magnetic field B and electric field E exist along y and negative z axis respectively. Under the influence of these fields a charge particle moves along OA undeflected. If electric field is switched off, find the pitch of helical trajectory in which the particle will move.

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$\frac{2 π m E}{q B^{2} \tan θ}$

$\frac{4 π m E}{q B^{2} \tan θ}$

$\frac{2 π m E}{q B^{2} \cot θ}$

$\frac{4 π m E}{a B^{2} \cot θ}$

answer is D.

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Detailed Solution

Since the particle is moving undeflected, so magnetic force = electric force

$\Rightarrow q v B \sin θ = q E \Rightarrow v = \frac{E}{B \sin θ}$

$Pitch, d = v \cos θ T = v \cos θ \frac{2 π m}{q B} = \frac{E}{B \sin θ} \cos θ \frac{2 π m}{q B} = \frac{2 π m E}{q B^{2} \tan θ}$

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