A uniform electric field exists in the region between two oppositely charged par

Question

A uniform electric field exists in the region between two oppositely charged parallel plates 1.65 cm apart. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate in a time interval 1.46×106 s .

a) Find the magnitude of the electric field.

Use 1.60×1019 C for the magnitude of the charge on an electron and 1.67×1027 kg for the mass of a proton.

b) Find the speed of the proton at the moment it strikes the negatively charged plate.

Explanation / Answer

(a)

First we will find the acceleration of the proton.

From kinetic equation of motion,

d = ut + (1/2) at2 = 0 + (1/2)at^2

0.0165 = (1/2)*a*(1.46*10(-6 ))^2

a = 1.548*10^10 m/s2

Force F = ma

F = qE

ma = qE

E = m a / q = [1.67*10(-27) * 1.548*10^10] / [1.60*10(-19)]

E = 161.58 N/C

(b)

Final speed of proton when it strikes the negatively charged plate,

v = u + a*t

v = 0 + 1.548*10^10 * 1.46*10(-6)

v = 2.26*10^4 m/s

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