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an electron with a speed of 5.00 x 10^8 cm/s enters an electric field of magnitude 1.00 x 10^3 N/C, traveling along field lines in the direction that s its motion.

a) How far will the electron travel in the field before stopping momentarily
b) how much time will have elapsed
c) in the region with the E field is only 8.00 mm long, what fraction of the electron's initial KE will be lost in that region?

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  1. F=ma
    F=eE
    ma = eE

    a=eE/m= 1.6•10⁻¹⁹•10³/9.1•10⁻³¹= =1.76•10¹⁴ m/s²
    s=v₀²/2a = v₀²m/2eE=
    =(5•10⁶)²•9.1•10⁻³¹/2•1.6•10⁻¹⁹•10³= =0.071 m

    v=v₀-at,
    v=0,
    t= v₀/a=5•10⁶/1.76•10¹⁴=2.84•10⁻ ⁸ s.

    s₁=(v₀²-v₁²)/2a,
    v₁² = v₀²-2s₁a.

    KE₁/KE₀=(m v₁²/2)/ (m v₀²/2) =
    = (v₁²/ v₀)² =( v₀²-2s₁a)/ v₀²=
    =1-(2s₁a/ v₀²)= 1- (2•8•10⁻³•1.76•10¹⁴/25•10¹⁶)=
    = 1-1.13•10⁻⁵=0.99999.

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