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

Question

A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, 1.80 cm distant from the first, in a time interval of 2.90×106 s .

a) Find the magnitude of the electric field. Express your answer with the appropriate units.

b) Find the speed of the proton when it strikes the negatively charged plate. Express your answer with the appropriate units.

Explanation / Answer

a)

d = distance between the plates = 1.80 cm = 0.018 m

t = time taken = 2.90 x 10-6 sec

Vo = initial speed = 0

a = acceleration = qE/m = (1.6 x 10-19) E/ (1.67 x 10-27) = 0.96 x 108 E m/s2

Using the equation

d = Vo t + (0.5) a t2

0.018 = 0 (2.90 x 10-6 ) + (0.5) (0.96 x 108 E) (2.90 x 10-6 )2

E = 44.6 N/C

b)

V = Vo + at = 0 + (0.96 x 108 x 44.6) (2.90 x 10-6 ) = 12416.64 m/s

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