Mathematical and Physical Journal
for High Schools
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Problem P. 4440. (April 2012)

P. 4440. A hemispherical insulating shell is charged positively, and is fixed. The charge distribution on the shell is uniform. At a point on the symmetry axis, which is exactly at a distance of the radius measured from the centre of the hemisphere O, a small negatively charged bead is released. The speed of the bead is v0 when it reaches the centre O.

What will the speed of the bead be when it reaches the shell? (Neglect the effect of gravity.)

(5 pont)

Deadline expired on May 10, 2012.

Sorry, the solution is available only in Hungarian. Google translation

Megoldásvázlat. A gyöngy végsebessége \sqrt{2}\,v_0. (Ez az eredmény akkor is érvényes, ha a gravitáció hatása nem hanyagolható el.)


16 students sent a solution.
5 points:Bolgár Dániel, Czipó Bence, Horváth András Levente, Janzer Olivér, Juhász Péter, Koncz Gabriella, Laczkó Zoltán Balázs, Nagy Lajos, Papp Roland, Szabó 928 Attila, Szélig Áron, Szigeti Bertalan György, Vajda Balázs.
3 points:1 student.
0 point:2 students.

Problems in Physics of KöMaL, April 2012