Charged pendulum · Estonian PhO 2015 #10

Physics · magnetostatics

Problem

A small charged ball of mass mm and charge qq is hanging at the end of a non-stretchable thread of length ll in a magnetic field of induction BB. The ball is brought to a height H=78lH=\frac{7}{8}l while holding the thread straight and then it is let free. The gravitational acceleration is gg and the direction of the magnetic field is perpendicular to the plane of the pendulum. It is also known that q2B2l=34m2gq^2B^2l=\frac{3}{4}m^2g applies. What is the trajectory of the ball? \begin{resizebox}{0.5\linewidth}{!}{ [diagram — see PDF] } \end{resizebox}

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