A parallel-plate capacitor is constructed from two square plates
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
A parallel-plate capacitor is constructed from two square plates, each of side length 0.20m, separated by a distance of 0.020m. The space between the plates is filled with air, and the plates are connected to a battery that maintains a constant potential difference of 400V. A small bead carrying charge q=−5.0μC is initially held against the positive plate (the plate at higher potential). An external agent then moves the bead very slowly along the central line perpendicular to the plates until it touches the negative plate.
(a) Calculate the magnitude and direction of the uniform electric field between the plates.
(b) Derive an expression for the magnitude of the external force that must be applied to the bead as a function of its distance y from the positive plate (0≤y≤0.020m) while it moves slowly across the gap.
(c) Using the result from part (b), integrate to obtain the total work done by the external agent in moving the bead from the positive to the negative plate. Provide a numerical value with appropriate units and sign.
(d) Verify that your answer in part (c) is consistent with the change in electric potential energy of the bead–field system.
(e) Draw and label a qualitative energy bar chart that represents the initial and final kinetic energy, potential energy, and work terms for the process described above.