Electric Potential

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What is the electric potential at a point 40 cm from a point charge of $+8$ nC in vacuum?

RankGuru · Accepted Answer

Electric potential due to a point charge is defined as the work done per unit positive charge in bringing a test charge from \infty to that point, given by $V = k\frac{q}{r}$, where $k = 9 \times 10^9$ N·m²/C². Unlike electric field, potential is a scalar quantity, making calculations simpler when only magnitudes are needed. Here, $q = 8 \times 10^{-9}$ C and $r = 0.40$ m. Substituting: $V = 9 \times 10^9 \times \frac{8 \times 10^{-9}}{0.40} = \frac{72}{0.40} = 180$ V. Option 90 V is incorrect because it corresponds to using $r = 0.80$ m, doubling the actual distance. Option 360 V is incorrect because it corresponds to halving the distance to $r = 0.20$ m. Option 45 V is incorrect because it results from misplacing a factor of 4 in the calculation. This is a direct NCERT application tested in JEE Main for electric potential due to a point charge. Plausibility check: 180 V at 40 cm from a nanocoulomb charge is consistent with standard textbook results, and the positive potential confirms the source is a positive charge.

Electric Potential

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