The answer you got is not correct; the correct answer is really ΔV = 8.4 x 107 V.

A Van de Graff generator is not the most satisfactory model to perform this analysis, because the electric field it establishes has a radial symmetry and the field lines are not parallel. In this situation, the force applied on the particle will be variable, and the mathematical approach is more complicated.

The simplest model to propose the solution of the problem is the movement of the particle in a uniform electric field, such as that established between two parallel metal plates with equal and opposite charges. In this case, the field is uniform and the force is constant; therefore, the calculation is reduced to one dimension.

In this way, we only have to match the electrostatic potential energy of the particle (qαΔV) and its kinetic energy (mαv2/2); then the equation is solved for the potential difference ΔV, keeping in mind that the velocity is 30% of the speed of light.

I hope this analysis clarifies your doubt about the procedure you have used in the solution.

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