Electrostatics with Conductors - AP Physics C Electricity and Magnetism

1. State the formula for capacitance of a parallel plate capacitor.

   $C = \frac{\varepsilon_0 A}{d}$. Capacitance depends on area, separation, and permittivity.

2. Identify the relation between capacitance and dielectric constant $k$.

   $C = kC_0$. Dielectric material increases capacitance by factor $k$.

3. What is the condition for a conductor's surface in electrostatic equilibrium?

   No net motion of charge. Static equilibrium means no current flows on conductor surface.

4. State Gauss's Law.

   $\oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enc}}}{\varepsilon_0}$. Relates electric flux through closed surface to enclosed charge.

5. What is the effect of a dielectric on the capacitance of a capacitor?

   It increases the capacitance. Dielectric reduces field, allowing more charge storage.

6. What is meant by electrostatic shielding?

   Blocking external electric fields. Conductor's free charges rearrange to cancel external fields inside.

7. What is the electric field due to a uniformly charged spherical shell outside it?

   $E = \frac{kQ}{r^2}$, for $r > R$. Outside shell, field acts as if all charge at center.

8. What is the electric potential inside a conductor in equilibrium?

   Electric potential is constant. No internal field means no potential variation inside.

9. What happens to excess charge on a conductor?

   It resides on the surface. Like charges repel, minimizing energy by spreading on surface.

10. What is the relationship between electric potential and electric field?

    $E = -\frac{dV}{dx}$. Field is negative gradient of potential in one dimension.

11. What is the principle behind shielding in conductors?

    Charges rearrange to cancel external fields. Mobile charges create fields that oppose external fields.

12. State the boundary condition for electric fields at a conductor's surface.

    $E_{\text{outside}} = \frac{\sigma}{\varepsilon_0}$. Field discontinuity equals surface charge density over $\varepsilon_0$.

13. Find the electric force on a charge $q$ in an electric field $E$.

    $F = qE$. Force equals charge times electric field strength.

14. What is the electric field just outside a charged conductor?

    Perpendicular to the surface. Field must be perpendicular due to conductor properties.

15. Calculate the electric field due to a point charge $q$ at distance $r$.

    $E = \frac{kq}{r^2}$. Coulomb's law: field decreases as inverse square of distance.

16. What is the effect of connecting a conductor to the ground?

    It neutralizes excess charge. Ground acts as infinite charge reservoir at zero potential.

17. What is true about the surface charge density on a conductor with irregular shape?

    Charge density is highest at sharp points. Sharp points create stronger fields, attracting more charge.

18. Find the charge on a capacitor given $C = 2 \mu F$ and $V = 5V$.

    $Q = CV = 10 \mu C$. Using $Q = CV$: $Q = (2 \times 10^{-6})(5) = 10 \mu C$.

19. What is the dielectric constant's effect on electric field strength?

    It reduces the field strength. Higher dielectric constant means weaker field for same charge.

20. Identify the concept of electric shielding.

    Conductors block external electric fields. Free electrons rearrange to cancel external fields inside.

21. What is the formula for the electric flux through a closed surface?

    $\Phi = \oint \mathbf{E} \cdot d\mathbf{A}$. Surface integral of electric field through closed surface.

22. Calculate the potential energy of a charge $q$ at potential $V$.

    Potential energy $U = qV$. Work done to bring charge from infinity to potential $V$.

23. State the equation for the electric potential energy between two point charges.

    $U = \frac{kq_1q_2}{r}$. Coulomb's law for potential energy between point charges.

24. What is the effect of grounding a conductor?

    Grounding neutralizes the conductor. Ground provides infinite charge reservoir at zero potential.

25. Determine the total capacitance for $C_1 = 2 \mu F$ and $C_2 = 3 \mu F$ in parallel.

    $C_{\text{total}} = C_1 + C_2 = 5 \mu F$. Parallel capacitors: total capacitance is sum of individual values.

26. Identify the relationship between electric field and surface charge density.

    $E = \frac{\sigma}{\varepsilon_0}$. Electric field just outside conductor surface in equilibrium.

27. What is the electric field at the center of a uniformly charged spherical shell?

    The electric field is zero. Symmetry: equal contributions from all surface elements cancel.

28. What is the effect of an external electric field on a conductor?

    It induces charge separation. Free charges redistribute to maintain zero internal field.

29. State the formula for the electric potential due to a point charge.

    $V = \frac{kq}{r}$. Coulomb's law for electric potential of point charge.

30. What happens to the potential difference across a conductor in equilibrium?

    The potential difference is zero. All points in conductor are at same potential.

31. Calculate the electric field between plates of a capacitor with $V = 12V$ and $d = 2m$.

    $E = \frac{V}{d} = 6 \text{ V/m}$. Uniform field between parallel plates: $E = V/d = 12/2$.

32. What is the unit for electric field?

    The unit is volts per meter (V/m). Derived from force per unit charge: $F/q$ has units N/C = V/m.

33. Determine the capacitance if two capacitors $C_1 = 2 \mu F$, $C_2 = 3 \mu F$ are in series.

    $C = \frac{1}{\frac{1}{C_1} + \frac{1}{C_2}} = 1.2 \mu F$. Series: $1/C = 1/2 + 1/3 = 5/6$, so $C = 6/5 = 1.2 \mu F$.

34. Calculate the total charge if capacitance $C = 4 \mu F$ and $V = 10V$.

    $Q = CV = 40 \mu C$. Using $Q = CV$: $Q = (4 \times 10^{-6})(10) = 40 \mu C$.

35. State the formula for the energy stored in a capacitor.

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

36. What is the electric field inside a conductor in electrostatic equilibrium?

    The electric field is zero. Free charges move to cancel internal fields in equilibrium.

37. Identify the charge distribution on a hollow conductor in equilibrium.

    Charge resides on the outer surface. Inner surface has zero charge in electrostatic equilibrium.

38. Calculate the energy stored in a capacitor with $C = 3 \mu F$ and $V = 9V$.

    $U = \frac{1}{2}CV^2 = 121.5 \mu J$. Using $U = \frac{1}{2}CV^2$: $U = \frac{1}{2}(3 \times 10^{-6})(81) = 121.5 \mu J$.

39. Find the electric field inside a hollow conductor carrying charge.

    The electric field is zero inside. Charges reside only on surfaces, creating zero internal field.

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