A charged particle $P$ leaves the origin with speed $v = v_{0}$ at some inclination with the $x -$ axis. There is a uniform magnetic field B along the $x -$ axis. $P$ strikes a fixed target $T$ on the $x -$ axis for a minimum value of $B = B_{0}$ . If the pitch of the helical path is equal to the maximum distance of the particle from the x-axis, then which of the following are not correct?

Question

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Answer 1

Time period of one revolution $= \frac{2 π m}{q B}$
$p i t c h = V_{h} \times T = \frac{2 π m}{q B} v cos θ$

Radius of the circle $r = \frac{m v sin θ}{q B}$

Max distance of the particle from the x-axis is 2r.

Since pitch is equal to 2r, $\frac{2 π m}{q B} v cos θ = 2 \frac{m v sin θ}{q B}$

$\Rightarrow tan θ = π$ .

Answer 2

Time period of one revolution

= \frac{2 π m}{q B}

p i t c h = V_{h} \times T = \frac{2 π m}{q B} v cos θ

Radius of the circle

r = \frac{m v sin θ}{q B}

Max distance of the particle from the x-axis is 2r.

Since pitch is equal to 2r,

\frac{2 π m}{q B} v cos θ = 2 \frac{m v sin θ}{q B}

\Rightarrow tan θ = π

.