Electric Potential Energy - AP Physics C Electricity and Magnetism

1. What does $U$ represent in electric potential energy calculations?

   Electric potential energy. Standard symbol for electric potential energy.

2. State how electric potential energy changes with increasing $r$ between two charges.

   Decreases. Inverse relationship between energy and separation distance.

3. State the formula for the change in electric potential energy.

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

4. Which equation relates electric potential energy to work done by the electric force?

   $W = -\triangle U$. Work by electric force equals negative change in potential energy.

5. What is electric potential energy if $q = 5\,C$, $V = 0\,V$?

   $U = 0\,J$. Using $U = qV = (5)(0) = 0\,J$.

6. Calculate electric potential energy for $q_1 = 2\,C$, $q_2 = -3\,C$, $r = 1\,m$.

   $U = -5.4 \times 10^{10}\,J$. Using $U = k_e\frac{q_1q_2}{r} = (8.99 \times 10^9)\frac{(2)(-3)}{1}$.

7. Identify the dependency of electric potential energy on charge sign.

   Depends on charge sign. Sign of charges affects whether energy is positive or negative.

8. Find $U$ if $q = 1\,C$, $E = 10\,N/C$, $d = 2\,m$.

   $U = -20\,J$. Using $U = -qEd = -(1)(10)(2) = -20\,J$.

9. How does electric potential energy relate to the work done by electric forces?

   $W = -\triangle U$. Conservation of energy principle for electric forces.

10. What happens to electric potential energy as two charges of opposite sign move closer?

    Decreases. Attractive forces lower potential energy as distance decreases.

11. What is the effect of doubling the charge on electric potential energy?

    Doubles. Energy scales linearly with charge magnitude.

12. Find the change in electric potential energy for $q = 1\,C$, $\triangle V = 4\,V$.

    $\triangle U = 4\,J$. Using $\triangle U = q\triangle V = (1)(4) = 4\,J$.

13. Calculate $U$ for $q_1 = 1\,C$, $q_2 = 1\,C$, $r = 2\,m$.

    $U = 4.5 \times 10^{9}\,J$. Using $U = k_e\frac{q_1q_2}{r} = (8.99 \times 10^9)\frac{(1)(1)}{2}$.

14. What is the effect of electric potential energy when a positive charge is moved against a field?

    Increases. Moving against field direction increases potential energy.

15. What is the formula for $U$ in terms of $E$, $q$, and $d$?

    $U = -qEd$. Standard formula for uniform field potential energy.

16. What is the relationship between electric potential energy and electric potential?

    $U = qV$. Energy equals charge times electric potential.

17. Which factor does not affect electric potential energy: charge, distance, or color?

    Color. Physical properties like color don't affect electric interactions.

18. Find electric potential energy if $q_1 = 1\,C$, $q_2 = 2\,C$, $r = 0.5\,m$.

    $U = 3.6 \times 10^{10}\,J$. Using $U = k_e\frac{q_1q_2}{r} = (8.99 \times 10^9)\frac{(1)(2)}{0.5}$.

19. State the constant $k_e$ in the formula for electric potential energy.

    $8.99 \times 10^9 \, N\, m^2/C^2$. Coulomb's constant in SI units.

20. What is the formula for the potential energy of an electric dipole in a uniform field?

    $U = -pE \, \cos \theta$. Dipole energy depends on alignment with external field.

21. State the formula for electric potential energy of a system of multiple charges.

    $U = k_e \sum \frac{q_i q_j}{r_{ij}}$. Sum over all charge pairs in the system.

22. What is the relation of electric potential energy to potential difference?

    Proportional. Energy changes linearly with potential difference.

23. What is the formula for electric potential energy of a point charge?

    $U = k_e \frac{q_1 q_2}{r}$. Coulomb's law for potential energy between two point charges.

24. What is $\theta$ in the formula for dipole potential energy $U = -pE \, \cos \theta$?

    Angle between $\vec{p}$ and $\vec{E}$. Orientation angle between dipole moment and electric field vectors.

25. What happens to electric potential energy when two like charges move closer?

    Increases. Like charges repel, so moving closer stores more energy.

26. In the formula $U = -pE \, \cos \theta$, what does $p$ represent?

    Electric dipole moment. Dipole moment magnitude in the potential energy formula.

27. How does electric potential energy change with distance between two charges?

    Inversely proportional. Energy decreases as $1/r$ when charges move apart.

28. Identify the unit of electric potential energy in the SI system.

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

29. Identify the symbol for electric potential energy.

    $U$. Standard symbol for electric potential energy.

30. State the condition for zero electric potential energy between two charges.

    Infinitely far apart. Reference point where potential energy equals zero.

31. Calculate electric potential energy for $q = 2\,C$, $V = 5\,V$.

    $U = 10\,J$. Using $U = qV = (2)(5) = 10\,J$.

32. What happens to electric potential energy when a charge moves parallel to equipotential?

    Remains constant. No work done moving along equipotential surfaces.

33. What is the electric potential energy of a charge in a uniform electric field?

    $U = -qEd$. Energy in uniform field depends on charge, field, and displacement.

34. Calculate the electric potential energy for $q = -3\,C$, $V = -2\,V$.

    $U = 6\,J$. Using $U = qV = (-3)(-2) = 6\,J$.

35. Which law is used to calculate the force in electric potential energy formulas?

    Coulomb's Law. Foundation for calculating electric forces and energies.

36. What is the relationship between electric potential energy and electric field?

    $U = -qEd$. Alternative form using electric field and displacement.

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