You measure the electric potential at various points between two charged paralle

Question

You measure the electric potential at various points between two charged parallel plates, along a straight line perpendicular to the surface of the plates. Points A, B, and C are 40 cm apart. You find that the voltage drops continuously from 8v at point A, to 3v at point B, to -2v at point C. a. Assume point A is at the origin and B and C are located on the +x-axis. Come up with a function f(x) that computes the voltage at any point on the axis. What is the voltage at x = 50cm? b. Find the magnitude and direction of E field in this region c. An electron is released from rest at point B. Does the electron travel toward point A or C? How fast is it moving when it gets there?

Explanation / Answer

a) Rate of dropping potential, V/x = (3 - 8) / 0.40 = -12.5 V/m

So, f(x) = 8 - 12.5x

At x = 0.50 m, f(x) = 8 - (12.5 * 0.50) = 1.75 V

b) E = -V/x = -(3 - 8) / 0.40 = 12.5 V/m

Electric field is in the direction of decreasing potential, so its in right direction.

c) Electron moves towards higher potential. So, electron will move towards A.

Acceleration of the electron, a = eE/me

Velocity of electron at A is given by,

v2 = 02 + [2 * (eE/me) * 0.40]

=> v = [2 * (1.6 * 10-19) * 12.5 * 0.40 / (9.1 * 10-31)]1/2 = 1.3 * 106 m/s

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