Between two large

PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance

Problem

Between two large, parallel metal plates separated by

5.0\,\text{cm}

, the electric potential varies with vertical position

y

according to the quadratic relation

V(y)= 200 - 20y + 0.50y^{2}

where

V

is in volts and

y

is in centimeters. The lower plate is at

y=0\,\text{cm}

and the upper plate is at

y=5.0\,\text{cm}

. Assume edge effects are negligible. (a) Determine the vertical position(s) between the plates where the magnitude of the electric field is zero. Show all work leading to your answer. (b) A small oil droplet of charge

+1.6\times10^{-19}\,\text{C}

is released from rest at

y=1.0\,\text{cm}

. Calculate the initial electric force (magnitude and direction) acting on the droplet. (c) Compare the electric field magnitude at

y=1.0\,\text{cm}

with that at

y=4.0\,\text{cm}

. Explain how this comparison is reflected in the shape of the potential function. (d) Suppose the potential function is adjusted so that

V(y)

becomes perfectly linear with the same values at the plates (

V=200\,\text{V}

y=0

and

V=185\,\text{V}

y=5.0\,\text{cm}

). Describe qualitatively how the motion of the same oil droplet released at

y=1.0\,\text{cm}

would differ from its motion in the original quadratic potential. Support your answer with reasoning tied to the electric field profile.

Related theory

Browse the problem library