When moving in an electric field, the electron’s speed increased from 1000 to 5000 km / s.

When moving in an electric field, the electron’s speed increased from 1000 to 5000 km / s. What is the potential difference passed by the electron?

Problem data: V0 (initial electron velocity) = 1000 km / s (in SI V0 = 1 * 10 ^ 6 m / s); V (speed after passing the potential difference) = 5000 km / s (in SI V = 5 * 10 ^ 6 m / s).

Constants: e (electron charge) = -1.6 * 10 ^ -19 C; m (electron mass) ≈ 9.11 * 10 ^ -31 kg.

The potential difference that the electron has passed is determined by the formula: e * Δφ = ΔEk = 0.5 * m * (V ^ 2 – V0 ^ 2), whence Δφ = 0.5 * m * (V ^ 2 – V0 ^ 2 ) / e.

Calculation: Δφ = 0.5 * 9.11 * 10 ^ -31 * ((5 * 10 ^ 6) ^ 2 – (1 * 10 ^ 6) ^ 2) / (-1.6 * 10 ^ -19) = 68.325 V.