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A particle having charge q is accelerated by a potential difference V. It would gain energy of _______.

Asked in GSEB Board July 2021 · Accelerated charges

• (1) (qV)/2
• (2) q²V
• (3) qV
• (4) (q²V)/2

Step-by-step solution

Why the other options are wrong

• (1) Borrows the 1/2 from the capacitor formula U = 1/2QV. There the voltage builds up from zero while charging; here the full V acts on the charge all the way, so the work is qV.
• (2) Dimensionally wrong: q²V has units C² V = C J, not joules. Energy gained is charge times potential difference, with q to the first power.
• (4) Two errors: the square on q (units C J, not energy) and the capacitor-style factor 1/2. The work done by the field is simply qV.

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