Electrostatics：練習問題

A positively charged rod is brought near an isolated, uncharged conducting sphere. Which of the following describes the charge distribution on the sphere?

Which of the following statements about equipotential surfaces is TRUE?

Two fixed positive point charges, \(Q_A = +9 \text{ nC}\) and \(Q_B = +4 \text{ nC}\), are separated by a distance of \(0.50 \text{ m}\). At what point along the line connecting the two charges, between them, is the electric potential a minimum?

(Given: \(1 \text{ nC} = 10^{-9} \text{ C}\))

A positively charged rod is brought near an isolated neutral metal sphere without touching it. Which of the following statements correctly describes the charge distribution on the sphere?

Two point charges, \(Q_1 = +4.5 \times 10^{-9} \text{ C}\) and \(Q_2 = -1.5 \times 10^{-9} \text{ C}\), are fixed at \((0 \text{ m}, 0 \text{ m})\) and \((0.03 \text{ m}, 0 \text{ m})\) respectively. Calculate the magnitude and direction of the net electric field at the point \(P(0 \text{ m}, 0.04 \text{ m})\).

(Given: Coulomb's constant \(k = 9.0 \times 10^9 \text{ N m}^2/\text{C}^2\))

When a glass rod is rubbed with a silk cloth, it becomes positively charged. In terms of the movement of microscopic particles, explain how the rod acquires this positive charge.

When a polythene rod is rubbed with a woolen cloth, the rod becomes negatively charged. In terms of electron transfer, state how the rod acquires this charge.

A parallel-plate capacitor with air between its plates has a capacitance of $$C_0$$. It is charged by a battery to a potential difference $$V_0$$, and then the battery is disconnected. A dielectric material with dielectric constant $$\kappa = 4.0$$ is then inserted to completely fill the space between the plates. Determine the ratio of the final energy stored to the initial energy stored in the capacitor.

A small plastic sphere with a mass of \(2.5 \times 10^{-4}\text{ kg}\) is suspended by an insulating thread in a uniform horizontal electric field of strength \(E\). The sphere carries a net charge of \(q = +5.0 \times 10^{-8}\text{ C}\). When the system is in equilibrium, the thread makes an angle of \(30^\circ\) with the vertical.

(a) Draw a free-body diagram of the sphere and label all the forces acting on it.
(b) Calculate the magnitude of the electrostatic force acting on the sphere.
(c) Determine the electric field strength \(E\).
(d) If the charge on the sphere is doubled while keeping the electric field constant, explain qualitatively how the angle of the thread will change.

(Take the acceleration due to gravity \(g = 9.81\text{ m s}^{-2}\))

Two large horizontal parallel metal plates are separated by a distance of \(0.05 \text{ m}\) in a vacuum. The upper plate is maintained at a potential of \(+600 \text{ V}\) while the lower plate is earthed.

(a) Calculate the magnitude and state the direction of the uniform electric field strength \(E\) between the plates.
(b) An oil droplet carrying a charge of \(-3.2 \times 10^{-18} \text{ C}\) is released from rest at a point exactly midway between the plates. Determine the magnitude and direction of the electrostatic force acting on the droplet.
(c) Calculate the work done by the electric field as the droplet moves from the midpoint to the upper plate.