= Solution
The <electron> moves in the direction for which the <electric field> does positive work. Its <kinetic energy> gain is the magnitude $eEL=30\,\mathrm{MeV}$. Hence
$$
\boxed{\gamma=1+\frac{30}{0.511}=59.7084,\qquad
\beta=\sqrt{1-\gamma^{-2}}=0.99985974.}
$$
This uses the <relativistic energy-momentum relation>, rather than the nonrelativistic kinetic-energy formula. <Acceleration> is opposite the field direction for a negatively charged <electron>, although the <energy> gain is positive along its actual displacement.
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