Mathematical and Physical Journal
for High Schools
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# Problem P. 4814. (February 2016)

P. 4814. A thin uniform ring of mass $\displaystyle M$ has a charge $\displaystyle +Q$ distributed uniformly on it. It is at rest in empty space with no force acting on it. A particle of mass $\displaystyle m$ and charge $\displaystyle +q$ is projected towards the ring along its axis from infinity with a speed $\displaystyle v_0$, the minimum speed required by the particle to pass through the ring. The particle passes through the ring to move to an infinite distance from it in the opposite side.

$\displaystyle (i)$ What is the minimum speed of the particle during its entire motion?

$\displaystyle (ii)$ What is the maximum speed of the ring during the entire event?

$\displaystyle (iii)$ What are the final speeds of the particle and the ring at the end of the event?

[Neglect any loss of energy by the system due to radiation.]

(4 pont)

Deadline expired on March 10, 2016.

### Statistics:

 24 students sent a solution. 4 points: Balogh Menyhért, Bekes Nándor, Büki Máté, Csorba Benjámin, Csuha Boglárka, Fehér 169 Szilveszter, Fekete Balázs Attila, Forrai Botond, Hornák Bence, Iván Balázs, Kasza Bence, Kormányos Hanna Rebeka, Körmöczi Dávid, Krasznai Anna, Németh Flóra Boróka, Olosz Adél, Szántó Benedek, Szentivánszki Soma , Szick Dániel, Tófalusi Ádám, Varga-Umbrich Eszter, Zöllner András. 2 points: 2 students.

Problems in Physics of KöMaL, February 2016