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A particle of mass m and charge q is travelling at a velocity v along x-axis at time t = 0. It enters a region in which electric field, E is present along z-axis and magnetic field, B is present along y-axis. The distance covered upto time $t = 0 .2 \times 10^{- 1}$ along x-axis is v/50 (in metres). Find the
value of v.

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$\frac{50 E}{B}$

$\frac{E}{50 B}$

$\frac{E}{20 B}$

$\frac{E}{B}$

answer is D.

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Detailed Solution

$v ⊥_{er} = - \frac{v_{0}}{2}$ will contribute to circular motion.

$v_{| |} = \frac{v_{0} \sqrt{3}}{2}$ will contribute to helical path.

$T = 2 π \frac{m}{B_{0} q}$

$Pitch, P = v_{| |} T = \frac{v_{0} \sqrt{3}}{2} T$

$Number of turns = \frac{R}{P} = \frac{v_{0} T \sqrt{3} (2)}{v_{0} \sqrt{3} T} = 2$

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