A charged particle is deflected by two mutually perpendicular oscillating electric fields such that the displacement of the particle due to each one of them is given by x $$=$$ A $$sin$$ $$($$ω$$t)$$ and y $$=$$ A $$sin$$ $$($$ω$$t+$$π$$6)$$ respectively. The trajectory followed by the charged particle is

Question

A charged particle is deflected by two mutually perpendicular oscillating electric fields such that the displacement of the particle due to each one of them is given by x $$=$$ A $$sin$$ $$($$ω$$t)$$ and y $$=$$ A $$sin$$ $$($$ω$$t+$$π$$6)$$ respectively. The trajectory followed by the charged particle is

Infinity Learn · Accepted Answer

When two SHM's (which$$ are perpendicular to each other $$) are given by $$x=A1sin$$ωt and $$y=A2sin($$ω$$t+$$δ$$)$$  and when they are combined, the trajectory of the particle is given $$byx2A12+y2A22-2xyA1A2cos$$δ$$=sin2$$δ (This$$ is equation of $$ellipse).For the given problem $$A1=A2=A$$ and δ$$=$$π$$6$$,$$x2A2+y2A2-2xyA2.32=14x2+y2-3xy$$ $$=$$ $$14A2$$ and this is an ellipse

A charged particle is deflected by two mutually perpendicular oscillating electric fields such that the displacement of the particle due to each one of them is given by $x = A \sin (ωt) and y = A \sin (ωt + \frac{π}{6})$ respectively. The trajectory followed by the charged particle is

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A charged particle is deflected by two mutually perpendicular oscillating electric fields such that the displacement of the particle due to each one of them is given by x = A sin (ωt) and y = A sin (ωt+π6) respectively. The trajectory followed by the charged particle is

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Ready to Test Your Skills?

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A charged particle is deflected by two mutually perpendicular oscillating electric fields such that the displacement of the particle due to each one of them is given by $x = A \sin (ωt) and y = A \sin (ωt + \frac{π}{6})$ respectively. The trajectory followed by the charged particle is