 Solution

ID: past-exam-of-the-theoretical-physics-i-course-of-the-university-of-cambridge/2018/1/c/solution

e E \neq = 0

, then

p (t) = e E t + O (1)

t \to \infty lim v (t) = c \frac{e E}{∣ e E ∣} .

The particle approaches the speed of light in the direction of the electric force, independently of its initial velocity. For positive

e

the limiting direction is along

E

; for negative

e

it is opposite. A massive particle never reaches that limiting speed in finite time. If the force is zero, the velocity remains

v_{0}

instead.

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