A) The electric field is constant and in the same direction as the electron's displacement, so the work done is given by:
W = Fd
W = work, F = electric force, d = displacement
The electric force on the electron is given by:
F = Eq
F = electric force, q = electron charge
Substitute F:
W = Eqd
Given values:
E = 442N/C, q = 1.6×10⁻¹⁹C, d = 3.50×10⁻²m
Plug in and solve for W:
W = 442(1.6×10⁻¹⁹)(3.50×10⁻²)
W = 2.48×10⁻¹⁸J
B) The electric field does work to move the electron. Apply the conservation of energy and you'll see that the electron's potential energy loss is equal to the work done by the field in moving the electron.
The electric potential energy change is -2.48×10⁻¹⁸J
C) Apply the work-energy theorem; the electron's kinetic energy equals the work done on it by the field.
KE = 0.5mv² = W
m = electron mass, v = velocity, W = work
Given values:
W = 2.48×10⁻¹⁸J, m = 9.11×10⁻³¹
Plug in and solve for v:
0.5(9.11×10⁻³¹)v² = 2.48×10⁻¹⁸
v = 2.33×10⁶m/s
