Electric fields：練習問題

An alpha particle (charge \( +2e \)) and a gold nucleus (charge \( +79e \)) are separated by a distance \( r \). If the alpha particle is moved such that the separation is halved to \( \frac{r}{2} \), by what factor does the electric potential energy of the system change?

A uniform electric field is created between two parallel plates separated by a distance \(d\). An electron (charge \(-e\), mass \(m\)) is released from rest at the negative plate. If the potential difference between the plates is \(V\), what is the time taken for the electron to reach the positive plate?

Consider two isolated point charges, \( Q_1 \) and \( Q_2 \), separated by a distance \( L \). The electric potential is zero at a point on the line joining them, at a distance \( \frac{L}{4} \) from \( Q_1 \). What is the ratio \( \frac{Q_1}{Q_2} \)?

Two identical conducting spheres carry charges of \( +3.0 \text{ nC} \) and \( -1.0 \text{ nC} \) respectively. They are brought into contact and then returned to their original positions. What is the ratio of the magnitude of the electrostatic force between them after contact to the magnitude of the force before contact?

In a radial electric field, the potential \( V \) at a distance \( r \) from a point charge is \( 100 \text{ V} \). The electric field strength at this same point is \( 50 \text{ V m}^{-1} \). What is the distance \( r \)?

Compare the magnitudes of the electrostatic force and the gravitational force between two protons separated by a distance \( r \). Explain why the gravitational force is usually neglected in subatomic interactions.