Acceleration of a charged particle in a uniform electric field

Two formulae are important.

E = F_el/q

(significance of the symbols: see electric field)

Δ E_kin  = q ΔV

• Δ E_kin  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.

1. Calculate the electric force on the electrons
2. Find the speed of the electrons at A.

a.   E = F_el /q

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

b.   q ΔV = Δ E_kin  

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

(1.6  X 10 ^-19)( 2.0 x 10²) = E_kin,A – E_kin,_K

3.2 x 10^-17 = ½ mv_A² – 0

3.2 x 10^-17 = ½ (9.1 x 10^-31) v_A²

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

v_A  = 8.4 x 10⁶ m/s