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 1.53 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 1.48 times 10^-6 s . Find the magnitude of the electric field. Use 1.60 times 10^-19 C for the magnitude of the charge on an electron and 1.67 times 10^-27 kg for the mass of a proton. Find the speed of the proton at the moment it strikes the negatively charged plate.

Explanation / Answer

PART - A

from the kinematics equations

using s = u t + 1 / 2 a t2

0.0153 = 0 + 1 / 2 X a X ( 1.48 X 10-6 ) 2

0.0153 = 0.5 X a X 2.19 X 10-12

a = 0.0153 / 0.5 X 2.19 X 10-12

a = 0.0153 / 1.095 X 10-12

a = 1.39 X 1010 m/s2

from nweton's second's law

we have F = ma

F = 1.67 X 1027 X 1.39 X 1010

F = 2.32 X 10-17 N

and finally to find the electric field we have

F = E Q

E = F / Q

E = 2.32 X 10-17 / 1.60 X 10-19

E = 145 N / C

PART - B

in the same above using on the kinematic equation for velocity is

V = u + a t

V = 0 + 1.39 X 1010 X 1.48 X 10-6

V = 20572 m / s

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