Electrostatic Potential: Point Charges, Potential Energy & Field Relation: 20 flashcards
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1. Define electric potential at a point.
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Electric potential at a point is the work done by an external agent in bringing a unit positive test charge from infinity to that point, without acceleration. It is a scalar quantity measured in volts (J/C).
2. Write the formula for electric potential due to a point charge $Q$ at distance $r$.
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$$V = \frac{KQ}{r}$$ where $K = \frac{1}{4\pi\varepsilon_0}$ and the sign of $Q$ is included.
3. What is the SI unit of electric potential and what does it equal in base units?
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The SI unit is the **volt (V)**, and $1\,\text{V} = 1\,\text{J/C}$ (one joule per coulomb).
4. How do you find the net potential at a point due to several charges?
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Use the algebraic sum: $$V_{net} = K\sum_i \frac{Q_i}{r_i}$$ Add each contribution with its sign — no vector resolution needed.
5. What is the electric potential at the midpoint between two equal and opposite charges $+Q$ and $-Q$ separated by $2x$?
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$V_{net} = \frac{KQ}{x} + \frac{K(-Q)}{x} = 0$. The scalars cancel, but the electric field there is **not** zero.
6. What is the electric potential at the midpoint between two identical charges $+Q$ separated by $2x$?
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$$V_{net} = \frac{KQ}{x} + \frac{KQ}{x} = \frac{2KQ}{x}$$ The two scalar contributions add.
7. Relate potential energy $U$ of a charge $q$ at potential $V$.
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$$U = qV$$ The sign of $q$ matters: a negative charge at positive $V$ has negative potential energy.
8. Define potential difference $\Delta V$ in terms of work.
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$$\Delta V = \frac{W}{q}$$ where $W$ is the work done **by an external agent** in moving charge $q$ slowly between the two points.
9. Write the expression for work done by an external agent in moving charge $q$ through potential difference $\Delta V$.
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$$W = q\,\Delta V$$ If $\Delta V = 0$ (equipotential), no net work is needed.
10. State the relation between electric field and potential as an integral.
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$$V = -\int \vec{E}\cdot d\vec{r}$$ The negative sign means the field points from high potential to low potential.
11. What does the negative sign in $V = -\int \vec{E}\cdot d\vec{r}$ physically mean?
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It means the electric field points from **high potential to low potential** — a positive charge released from rest accelerates toward lower $V$.
12. For a uniform field $E$ over distance $d$ along the field, what is $|\Delta V|$?
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$$|\Delta V| = Ed$$ This is why electric field can be expressed in volts per metre (V/m) as well as N/C.
13. Does zero electric potential at a point imply zero electric field there? Give an example.
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**No.** At the midpoint between $+Q$ and $-Q$, $V=0$ but $\vec{E}\neq 0$ (both fields point the same way). Potential is a scalar sum; field is a vector sum.
14. Does zero electric field at a point imply zero potential there? Give an example.
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**No.** At the midpoint between two identical charges $+Q$, $E=0$ but $V = \frac{2KQ}{x} \neq 0$.
15. How does a positive charge move spontaneously in a potential landscape? What about a negative charge?
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A **positive** charge moves spontaneously from **high to low** potential. A **negative** charge moves from **low to high** potential.
16. What is an equipotential surface, and what is the work done moving a charge along it?
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A surface on which every point has the same potential. Moving a charge along it involves **zero** change in potential, so no net work is done ($\Delta V = 0$).
17. Is electric potential a property of the source charges or of the test charge?
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It is a property of the **source charge configuration**, independent of the test charge. That is why you can compute $V$ once and reuse it for any charge placed there.
18. What is the work done **by the electric field** when charge $q$ moves through potential difference $\Delta V$?
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$$W_{field} = -q\,\Delta V$$ This is opposite in sign to the work done by an external agent ($W_{ext} = q\,\Delta V$).
19. Why is potential computationally easier to use than electric field for multiple charges?
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Because $V$ is a **scalar**: contributions add algebraically with signs, with no components, angles, or vector resolution required.
20. Give two real-world applications that rely on electric potential.
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**Circuit theory** (voltage is potential difference) and **capacitor design** (energy stored $\tfrac12 CV^2$ builds on $U=qV$). Also electron optics, CRT displays, and ECG.
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