Electric Potential Energy - AP Physics 2

1. If $q = 5 \text{ C}$, $E = 10 \text{ N/C}$, $d = 2 \text{ m}$, find $U$.

   $U = 100 \text{ J}$. Direct substitution: $U = 5 \times 10 \times 2 = 100$ J.

2. State the potential energy of a dipole in a uniform electric field.

   $U = -pE \text{ cos } \theta$. Energy depends on dipole alignment relative to field direction.

3. What is the relationship between equipotential surfaces and electric field lines?

   They are perpendicular to each other. Electric field always points perpendicular to equipotential surfaces.

4. What is the potential energy difference if a charge $q$ moves through a potential difference $V$?

   $\triangle U = q\triangle V$. Change in potential energy equals charge times potential difference.

5. State the relationship between electric potential ($V$) and electric potential energy ($U$).

   $U = qV$. Direct relationship between potential energy and electric potential.

6. If $U = 50 \text{ J}$ and $q = 2 \text{ C}$, what is $V$?

   $V = 25 \text{ V}$. Solving $U = qV$ for potential: $V = \frac{50}{2} = 25$ V.

7. What is the electric potential energy of a charge at infinity?

   Zero, as potential energy approaches zero at infinity. Infinity serves as the standard reference point for potential energy.

8. Define electric potential.

   Electric potential is the potential energy per unit charge. Potential energy divided by charge gives potential at a point.

9. Calculate the potential energy: $p = 2 \text{ C} \text{ m}$, $E = 3 \text{ N/C}$, $\theta = 0^\text{o}$.

   $U = -6 \text{ J}$. With $\theta = 0°$: $U = -2 \times 3 \times 1 = -6$ J.

10. What happens to electric potential energy when opposite charges are brought closer?

    Electric potential energy decreases. Attractive force releases energy as charges approach each other.

11. What is zero electric potential energy?

    Reference point where potential energy is defined as zero. Arbitrary reference point chosen for convenience in calculations.

12. Calculate potential energy change: $q = 2 \text{ C}$, $\triangle V = 5 \text{ V}$.

    $\triangle U = 10 \text{ J}$. Direct calculation: $\triangle U = 2 \times 5 = 10$ J.

13. What is the formula for the potential energy stored in a capacitor?

    $U = \frac{1}{2} CV^2$. Standard formula for energy stored in capacitor electric field.

14. What is the potential energy change if a charge moves in a radial electric field?

    Calculated using $U = k_e \frac{q_1 q_2}{r}$. Use the two-point charge formula for radial field configurations.

15. For a charge $q$ in a field $E$, what is the work done moving it a distance $d$?

    $W = -qEd$. Negative sign indicates work done against the electric field.

16. State the potential energy formula for a point charge $q$ in a potential $V$.

    $U = qV$. Fundamental relationship between charge, potential, and potential energy.

17. What does a negative electric potential energy indicate about the interaction between charges?

    Attractive interaction between opposite charges. Opposite charges attract, releasing energy when brought together.

18. What is the potential energy formula for a capacitor with capacitance $C$ and voltage $V$?

    $U = \frac{1}{2} CV^2$. Energy stored in electric field between capacitor plates.

19. What is the expression for electric potential energy in a uniform field?

    $U = qEd$. Formula for potential energy in constant electric field.

20. What happens to electric potential energy when like charges are brought closer?

    Electric potential energy increases. Repulsive force requires work to decrease separation distance.

21. Calculate the potential energy of a capacitor: $C = 4 \text{ F}$, $V = 5 \text{ V}$.

    $U = 50 \text{ J}$. Using $U = \frac{1}{2} \times 4 \times 5^2 = 50$ J.

22. What is electric potential energy?

    Energy stored in a system due to electric forces. Energy from charge interactions and positions in electric fields.

23. What is the electric potential energy change for a charge moving through a potential difference?

    $\triangle U = q \triangle V$. Change in potential energy from moving through potential difference.

24. What is the electric potential energy of a charge $q$ at a potential $V$?

    $U = qV$. Direct application of the potential energy-potential relationship.

25. In a capacitor, how does increasing the separation affect potential energy?

    Increases potential energy. Larger separation increases energy stored in electric field.

26. Find the potential energy of a system with $q_1 = 1 \text{ C}$, $q_2 = 2 \text{ C}$, and $r = 0.5 \text{ m}$.

    $U = 35.96 \times 10^9 \text{ J}$. Using $U = 8.99 \times 10^9 \times \frac{1 \times 2}{0.5}$.

27. What is the electric potential energy of a system of two point charges $q_1$, $q_2$ separated by $r$?

    $U = k_e \frac{q_1 q_2}{r}$. Standard two-charge potential energy formula from Coulomb's law.

28. Calculate the work done: $q = 4 \text{ C}$, $E = 5 \text{ N/C}$, $d = 3 \text{ m}$.

    $W = -60 \text{ J}$. Direct calculation: $W = -4 \times 5 \times 3 = -60$ J.

29. Define equipotential surface.

    Surface where electric potential is constant. Surface of points having identical electric potential values.

30. What is the unit of electric potential energy in the SI system?

    Joule (J). Standard SI unit for all forms of energy.

31. What does a positive electric potential energy indicate about the interaction between charges?

    Repulsive interaction between like charges. Same charges repel, requiring energy to bring them together.

32. Calculate the electric potential energy: $q_1 = 2 \text{ C}$, $q_2 = 3 \text{ C}$, $r = 1 \text{ m}$.

    $U = 5.394 \times 10^{10} \text{ J}$. Using $U = k_e \frac{q_1 q_2}{r} = 8.99 \times 10^9 \times \frac{2 \times 3}{1}$.

33. Calculate potential energy: $q = 3 \text{ C}$, $V = 4 \text{ V}$.

    $U = 12 \text{ J}$. Direct substitution: $U = 3 \times 4 = 12$ J.

34. What is the potential energy of a charge $q$ in the presence of a uniform electric field $E$?

    $U = qEd$. Energy stored when charge is displaced distance $d$ in uniform field.

35. State the formula for electric potential energy between two point charges.

    $U = k_e \frac{q_1 q_2}{r}$. Direct formula from Coulomb's law for two point charges.

36. Identify the constant $k_e$ in the formula $U = k_e \frac{q_1 q_2}{r}$.

    Coulomb's constant, $8.99 \times 10^9 \text{ N m}^2/\text{C}^2$. Fundamental constant relating electric force and charge separation.

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