Question

When an electron moves from rest against a uniform electric field a distance of 10.0 cm it attains a speed v. If it moves an additional 10.0 cm, the final speed is:

Select one: 1.4 v

0.7 v

2.0 v

v

4.0 v

Answer 1

From energy conservation,

dU + dK = 0

dK = -dU

here, dK = change in kinetic energy

dU = change in electric potential energy

For initial 10.0 cm,

dK = KEf - KEi = 0.5*m*v^2 - 0

dU = -q*dV = q*(E*d)

given, m = mass of electron

q = charge on electron

E = electric field

d = distance traveled = 10.0 cm

v = final speed

then, 0.5*m*v^2 = q*E*d

E = 0.5*m*v^2/(q*d)

Now, by again applying energy conservation for total 20.0 cm,

dK = KEf - KEi = 0.5*m*v'^2 - 0

dU = -q*dV = q*(E*d')

here,

d' = total distance traveled = 10.0 + 10.0 = 20.0 cm

v' = final speed after 20.0 cm = ??

then, 0.5*m*v'^2 = q*E*d'

0.5*m*v'^2 = q*[0.5*m*v^2/(q*d)]*d'

v'^2 = (d'/d)v^2

v'^2 = (20/10)*v^2 = 2*v^2

v' = sqrt(2)*v

v' = 1.4 v

So, correct option is A.

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