An electron and a proton are placed in the same uniform electric field. What is the ratio of the magnitude of the acceleration of the electron to that of the proton?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Equal to the ratio of the mass of the proton to the mass of the electron
The electron and the proton carry charges of the same magnitude \( e \). So in the same field \( E \), both feel a force of the same magnitude \( eE \). The acceleration \( a=eE/m \) is then inversely proportional to the mass.
\( a_e=eE/m_e \)
\( a_p=eE/m_p \)
\( \begin{aligned} \frac{a_e}{a_p} &= \frac{eE/m_e}{eE/m_p} \\ &= \frac{m_p}{m_e} \end{aligned} \)
Therefore, the lighter electron has the larger acceleration, about 1836 times that of the proton, and the forces act in opposite directions.