Solution to the May, 2018 Challenge, Impulse
          Control

doi:10.1119/1.5055313

Let $\vec{F_{r}}$ ⁠, ${\vec{F}}_{L}$ ⁠, respectively, be the resistive force and the Lorentz force, v₀ is the initial speed of the charged particle. Also, l₀ = 20 cm and l₁ = 12 cm, B is the magnitude of the initial magnetic field, and l₂ is the distance from the entry point to the position which particle stops if the magnitude of the magnetic field is $B_{2} = \frac{B}{2}$ ⁠.

Applying Newton’s 2^nd law, we have:

{\vec{F}}_{r} + {\vec{F}}_{m} = m \vec{a}

- k \vec{v} + q [\vec{v} \times \vec{B}] = m \vec{a}

- k \vec{v} d t - q [\vec{B} \times \vec{v} d t] = m \vec{a} d t

- k d \vec{s} - q [B...

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Solution to the May, 2018 Challenge, Impulse Control

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