Electric Potential

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.