Mathematical and Physical Journal
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# Problem P. 4181. (September 2009)

P. 4181. The width of the uniform magnetic field, shown in the figure, is =5 cm, the induction of the field is B=0.167 T. A proton enters into the field perpendicularly to the field lines, and after passing the magnetic field it is deflected by an angle of =30o.

a) Determine the speed v0 of the proton and the time while it passes the magnetic field.

b) What voltage is to be applied in order to stop the proton in a distance of s=10 cm, and how long does it take to stop the proton?

c) Suppose that another proton enters into the magnetic field at a speed of v1=2.106 m/s, and at the angle , shown in the figure. What is the least angle , if the particle bounces back from the magnetic wall?

(5 pont)

Deadline expired on October 12, 2009.

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

$\displaystyle {\bf Megoldás.} a)$ $\displaystyle 1{,}6\cdot10^6~\frac{{\rm m}}{\rm s},$ illetve $\displaystyle 3{,}3\cdot 10^{-8}~\rm s.$

$\displaystyle b)$ $\displaystyle 13{,}3~\rm kV.$

$\displaystyle c)$ $\displaystyle \alpha>36{,}9^\circ$

### Statistics:

 70 students sent a solution. 5 points: Balogh Gábor, Balogh Tamás, Béres Bertold, Bodnár Dávid, Budai Ádám, Csopor Dávid, Filep Gábor, Fonai Dániel, Galzó Ákos Ferenc, Garaguly Gergő, Hartstein Máté, Illés Dorottya, Janosov Milán, Knódel Máté, Kovács Attila, Kovács Benjámin, Krämer Zsolt, Kungl Ákos Ferenc, Laczkó Zoltán Balázs, Lőrincz Dóra, Molnár Alexandra, Ölvedi Balázs, Pál Domonkos, Pálovics Péter, Patartics Bálint, Pázmán Koppány, Szabó 928 Attila, Trényi Róbert, Varju 105 Tamás, Várnai Péter, Vécsey Máté, Zelei Kristóf, Zsámboki Richárd. 4 points: Batki Bálint, Bolgár Dániel, Börcsök Bence, Burján Bence, Csóré András, Kovács 616 Philip, Kovács Attila, Köpenczei Gergő, Lájer Márton, Mayer Martin János, Neumer Tamás, Roboz Klaudia, Szikszai Lőrinc, Tamási Mátyás. 3 points: 9 students. 2 points: 8 students. 1 point: 3 students. 0 point: 2 students. Unfair, not evaluated: 1 solution.

Problems in Physics of KöMaL, September 2009