electric potential

Question

A charge of +5 nC is moved from infinity to a point where the potential is 100 V. How much work is done?

RankGuru · Accepted Answer

1. **Work-Potential Relation**: The external work done ($W$) in moving a charge $q$ is the product of charge and potential difference.
   - $W = q(V_{final} - V_{initial})$.
2. **Identify State**:
   - At infinity, potential is zero ($V_{initial} = 0$).
   - Final potential $V = 100 	ext{ V}$.
   - Charge $q = 5 	imes 10^{-9} 	ext{ C}$ ($5$ nC).
3. **Calculation**:
   - $W = 5 	imes 10^{-9} 	imes (100 - 0)$
   - $W = 5 	imes 10^{-7} 	ext{ Joules}$.
4. **Note**: This work is positive, meaning external energy was required to bring the positive charge towards another positive source.

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