Physics
Physics
Problem
A researcher connects a parallel-plate capacitor to a battery. The capacitor consists of two circular plates, each of radius , separated by . Air fills the space between the plates. Assume the electric field is uniform and edge effects are negligible. a) Calculate the magnitude of the electric field between the plates. b) A singly ionized sodium ion () is released from rest midway between the plates. Determine both the magnitude and direction of the electric force acting on the ion. c) Compute the capacitance of the device. d) Determine the energy stored in the capacitor when it is fully charged by the battery, and express that energy as an energy density (energy per unit volume) inside the region between the plates.Intuitive explanation
The key is recognizing that a parallel-plate capacitor's behavior depends on its geometry and the voltage applied. You'll need to find the capacitance first using the plate area and separation, then use to find the charge stored, and to find the electric field strength. The uniform field assumption means the voltage drops linearly across the gap—a powerful simplification that lets you treat this as a straightforward geometry problem.
Intuitive explanation
The key is recognizing that a parallel-plate capacitor's behavior depends on its geometry and the voltage applied. You'll need to find the capacitance first using the plate area and separation, then use to find the charge stored, and to find the electric field strength. The uniform field assumption means the voltage drops linearly across the gap—a powerful simplification that lets you treat this as a straightforward geometry problem.