Work And Energy In Electric Field

When a charged particle is accelerated through a potential difference (V), the work done on it equals the change in kinetic energy by the work-energy theorem: (W = qV = \Delta KE). Since the proton starts from rest, all work goes into kinetic energy: (KE = qV). The proton carries charge (q = e = 1.6 \times 10^{-19}) C and is accelerated through (V = 1500) V. Substituting: (KE = 1.6 \times 10^{-19} \times 1500 = 2.4 \times 10^{-16}) J. This can also be expressed as (1500) eV (electron-volts), confirming the result since 1 eV = (1.6 \times 10^{-19}) J. Option (1.6 \times 10^{-16}) J is incorrect because it omits the factor of 1500 in the multiplication. Option (2.4 \times 10^{-19}) J is incorrect because it uses (V = 1) V (i.e., ignores the 1500 multiplier). Option (1.6 \times 10^{-19}) J is the charge of the proton in coulombs, not the kinetic energy. This NCERT application of the work-energy theorem to charged particles is a fundamental JEE Main topic. Plausibility check: (2.4 \times 10^{-16}) J corresponds to 1500 eV, consistent with proton energies in low-voltage accelerators.