A beam of alpha particles (charge

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential

Problem

+2e

, mass

m_{\alpha}=6.64\times10^{-27}\,\text{kg}

) is first accelerated through a potential difference of

4.0\,\text{kV}

and then enters a second accelerating region. The design goal is for the particles to emerge from the second region with a speed of

9.0\times10^{5}\,\text{m}\,\text{s}^{-1}

. Neglect any forces other than those due to the applied electric fields. (a) Determine the speed of an alpha particle after the first

4.0\,\text{kV}

acceleration. (b) Calculate the additional potential difference required in the second region so that the particle exits with the desired final speed. (c) Explain how your answer to part (b) would change, if at all, if the first accelerating stage had provided

6.0\,\text{kV}

instead of

4.0\,\text{kV}

. Justify your response without repeating the full calculation.

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