Acceleration of a charged particle in a uniform electric field

Two formulae are important.

E = Fel/q

(significance of the symbols: see electric field)

Δ Ekin  = q ΔV

  • Δ Ekin  change of the kinetic energy in  J
  • q          charge in C
  • ΔV       potential difference in  V or J/C

Example

Electrons are accelerated between the negative plate K

and the positive plate  A                                                                               

The potential difference between the plates is  2.0 x 102 V

The electric field is 5.0 x 102 N/C

The velocity  speed of the electrons at K is negligible.

Acceleration of a charged particle in a uniform electric field
  1. Calculate the electric force on the electrons
  2. Find the speed of the electrons at A.

a.   E = Fel /q

Fel = q E = ((1.6 x 10-19)(5.0 x 10 2))= 8.0 x 10-17 N.

b.   q ΔV = Δ Ekin  

(At acceleration  : q ΔV > 0 ;   at delay :  q ΔV <0)

(1.6  X 10 -19)( 2.0 x 102) = Ekin,A – Ekin,K

3.2 x 10-17 = ½ mvA2 – 0

3.2 x 10-17 = ½ (9.1 x 10-31) vA2

vA 2 = (3.2 x 10-17)/(4.55 x 10-31)

vA  = 8.4 x 106 m/s

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