Electric Potential Point Charge

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Potential at distance r from isolated charge Q (zero at infinity)?

RankGuru · Accepted Answer

1. **Definition**: Electric potential ($V$) at a point is the amount of work done in moving a unit positive charge from infinity to that point against the electrostatic forces.
2. **Integral Relation**: $V = -\int_{\infty}^r E \cdot dr$.
3. **Calculation**:
   - $V = -\int_{\infty}^r \frac{kQ}{x^2} dx = -kQ [-\frac{1}{x}]_{\infty}^r$
   - $V = kQ [\frac{1}{r} - 0] = \frac{kQ}{r}$
4. **Result**: The potential is a scalar quantity given by **$V = kQ/r$**.

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Electric Potential Point Charge

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