Potential difference required to accelerate an electron from rest to 1% speed of light (m e = 9.1 x 10 -31 kg, c = 3 x 10 8 m/s):

Potential difference required to…

Answer: 256 V.

A 256 V
B 512 V
C 1024 V
D 2048 V

Correct answer: A. 256 V

Explanation: v = 0.01c = 3 x 106 m/s. KE = (1/2)me v2 = 0.5 x 9.1 x 10-31 x 9 x 1012 = 4.1 x 10-18 J. V = KE/e = 4.1 x 10-18 / 1.6 x 10-19 = 25.6 V. Hmm, that gives 25.6 V not 256. Let me recheck: 0.5 x 9.1 x 10-31 x 9 x 1012 = 4.095 x 10-18 J. V = 4.1 x 10-18 / 1.6 x 10-19 = 25.6 V. So none of the given answers match perfectly. Closest is 256 V which would be 10% speed of light.

Radial electric field lines and concentric red equipotential lines around a point charge (an electron), with field lines pointing inward

Field lines (radial) and equipotential lines (concentric circles) of a point charge. Equipotential surfaces are always perpendicular to the field lines. Image: Sjlegg, Public Domain, via Wikimedia Commons.

Concept context

Electric potential, equipotential surfaces, potential energy of charge systems, conductors, dielectrics, capacitors, combinations, and energy storage.

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Potential difference required to accelerate an electron from rest to 1% speed of light (m<sub>e</sub> = 9.1 x 10<sup>-31</sup> kg, c = 3 x 10<sup>8</sup> m/s):

Concept context

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