A particle of charge q and mass m is subjected to an electric field $$E=E01$$−$$ax2$$ in the $$x-direction$$, where a and $$E0$$ are constants. Initially the particle was at rest at x $$=$$ $$0$$. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is:

Question

A particle of charge q and mass m is subjected to an electric field $$E=E01$$−$$ax2$$  in the $$x-direction$$, where a and  $$E0$$ are constants. Initially the particle was at rest at x $$=$$ $$0$$. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is:

Infinity Learn · Accepted Answer

From $$work-energy$$ $$theoremdK=dW=qEdx=qE01-ax2dx$$∴Δ$$K=qE0$$∫$$0x1-ax2dx$$ $$=qE0x-ax33=0$$ ⇒$$x1-a3x2=0$$⇒$$x=0$$,±$$3a$$

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