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The electric potential (V) due to a point charge (q) at a distance (r) in a vacuum is given by the formula:
[ V = frac{1}{4piepsilon_0} cdot frac{q}{r} ]
where (epsilon_0) is the vacuum permittivity constant, approximately equal to (8.85 times 10^{-12} , text{C}^2/text{N}cdottext{m}^2).
The potential difference (Delta V) between two points due to a point charge is the difference in the electric potentials at those two points, given by:
[ Delta V = V_2 – V_1 ]
Considering the point charge of (0.4 text{nC}) (or (0.4 times 10^{-9} , text{C})) located at ((2, 3, 3)) meters, we want to find the potential difference between points ((2, 3, 3)) meters and ((-2, 3, 3)) meters.
### Calculation
1. Distance of the first point from the charge:
The first point is the location of the charge itself, so (r_1 = 0).
– For practical purposes, the potential at the location of a point charge is infinite, but since we’re calculating a
c
Explanation: Vab = (Q/4πεo)(1/rA) + (1/rB), where rA and rB are position vectors rA =
1m and rB = 4m. Thus Vab = 2.7 volts.