Electric Fields - AP Physics C Electricity and Magnetism

1. What is the electric field inside a spherical shell of charge?

   Zero. No charge inside means zero enclosed charge.

2. State the electric field due to an infinite plane of charge with density $\sigma$.

   $E = \frac{\sigma}{2\varepsilon_0}$. Field from single infinite charged plane.

3. State the relationship between electric field $E$ and electric force $F$ on a charge $q$.

   $F = qE$. Electric field is force per unit charge.

4. Identify the formula for the electric field between two parallel plates with charge density $\sigma$.

   $E = \frac{\sigma}{\varepsilon_0}$. Uniform field between infinite parallel plates.

5. What is the formula for the torque $\tau$ on a dipole in a uniform electric field $E$?

   $\tau = pE\sin\theta$. Torque depends on field strength and dipole orientation.

6. State the relationship between electric field $E$ and electric potential $V$.

   $E = -\frac{dV}{dr}$. Field is negative gradient of potential.

7. Identify the SI unit for electric field.

   Newton per Coulomb (N/C). Force per unit charge, equivalent to V/m.

8. What is the electric field inside a uniformly charged sphere?

   $E = \frac{kQr}{R^3}$ for $r<R$. Field inside sphere increases linearly with radius.

9. What is the effect on the electric field if the charge density on a surface is doubled?

   Electric field doubles. Field is directly proportional to surface charge density.

10. What is the value of the permittivity of free space $\varepsilon_0$?

    $8.85 \times 10^{-12} \text{ C}^2/\text{N} \cdot \text{m}^2$. Fundamental constant relating electric flux to charge.

11. State the formula for the electric field due to a line charge with linear density $\lambda$.

    $E = \frac{\lambda}{2\pi\varepsilon_0r}$. Cylindrical symmetry gives perpendicular field from Gauss's law.

12. What is the electric field at the midpoint between two equal positive charges?

    Zero. Equal charges create equal and opposite fields that cancel.

13. What is the electric field at a point on the axis of a charged ring?

    $E = \frac{kQz}{(z^2 + R^2)^{3/2}}$. Axial field component from ring geometry.

14. What happens to the electric field strength if the distance from a point charge is doubled?

    Reduces by a factor of 4. Electric field follows inverse square law.

15. How does the electric field behave in a non-conducting material?

    Field lines pass through the material. Field penetrates non-conducting materials unchanged.

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

    Zero. Free charges redistribute to cancel internal fields.

17. What is the direction of the electric field vector at a point in space?

    Direction of the force on a positive test charge. Field direction defined by positive test charge motion.

18. What happens to the electric field if the medium between charges is replaced by a dielectric?

    Field decreases. Dielectric reduces field by factor of dielectric constant.

19. Identify the electric field expression for a dipole at a point along its axis.

    $E = \frac{1}{4\pi\varepsilon_0} \cdot \frac{2p}{r^3}$. Axial field for dipole with moment $p$.

20. What is the formula for the electric field $E$ due to a point charge $q$?

    $E = \frac{kq}{r^2}$. Coulomb's law for electric field, where $k = \frac{1}{4\pi\varepsilon_0}$.

21. What is the electric field due to a uniformly charged sphere outside its radius?

    $E = \frac{kQ}{r^2}$. Outside sphere, field acts like point charge at center.

22. What is the direction of the electric field from a positive charge?

    Radially outward. Field points away from positive charges.

23. What is the force on a charge $q$ in an electric field $E$ if $q = 0$?

    Zero. Force equals charge times field; zero charge gives zero force.

24. What is the electric field halfway between two equal but opposite point charges?

    Non-zero, directed from positive to negative charge. Fields from opposite charges add constructively between them.

25. State Gauss's Law in integral form.

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

26. Identify the electric field at the center of a uniformly charged ring.

    Zero. Symmetry cancels all field contributions at center.

27. Find the electric field magnitude 1 m away from a $1 \text{ C}$ point charge.

    $E = 9 \times 10^9 \text{ N/C}$. Using $E = \frac{kq}{r^2}$ with $k = 9 \times 10^9$.

28. Find the electric field at a point $3 \text{ m}$ away from a $2 \text{ C}$ charge.

    $E = 2 \times 10^9 \text{ N/C}$. Using $E = \frac{kq}{r^2} = \frac{(9 \times 10^9)(2)}{9}$.

29. If the charge on a point is tripled, what happens to the electric field strength at a fixed point?

    Triples. Electric field is directly proportional to source charge.

30. What is the net electric field in a region with two equal opposite uniform fields?

    Zero. Equal magnitude opposite fields cancel completely.

31. State the principle of superposition for electric fields.

    The net field is the vector sum of individual fields. Individual fields add vectorially at each point.

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

    $E = \frac{\sigma}{\varepsilon_0}$. Surface charge creates field proportional to density.

33. What is the effect on electric field strength if charge and distance both double?

    No change. Doubling both charge and distance keeps $\frac{q}{r^2}$ constant.

34. What happens to the electric field if the charge on a point source is halved?

    Reduces by a factor of 2. Electric field is directly proportional to source charge.

35. What is the direction of the electric field from a negative charge?

    Radially inward. Field points toward negative charges.

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