An electron is initially at rest in space. An electric field is suddenly turned

Question

An electron is initially at rest in space. An electric field is suddenly turned on around the electron. Eventually the electron moves far away from the electric field and reaches a velocity of 2.5x10^5 m/s. What was the absolute value of the potential difference that accelerated the electron? Give your answer in volts. In the previous question, suppose that an electric field exist between two points of potential difference of loo V. These two points have a separation of 3.0 mm. What is the value of the electric field at point 2.5 mm from the first point? Give your answer in newtons per coulomb to 2 significant figures.

Explanation / Answer

(a)

velocity at any instant of time will be

v = u + a t

as the electron is started from rest

u = 0

v = a t

= (q E / m) t since a = (q E / m)

= (q V / d m) t since V = Ed, E = V / d

= (q V / v t m) t since v = d / t, d = v t

then finally we get

v2 = q V / m

V = m v2 / q

m is the mass of electron

m = 9.11 x 10-31 kg

q is charge on the electron

q = 16 x 10-20 C

solve to get the potential difference

(b)

for the second part we use

V = E d

d is seperation

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