AP Physics C E&M- 10.1 Electrostatics with Conductors- Study Notes- New Syllabus
AP Physics C E&M- 10.1 Electrostatics with Conductors – Study Notes
AP Physics C E&M- 10.1 Electrostatics with Conductors – Study Notes – per latest Syllabus.
Key Concepts:
- Charge Distribution Within a Conductor
Charge Distribution Within a Conductor
An ideal conductor is a material in which electrons can move freely in response to electric forces. When charges are placed on a conductor, they quickly redistribute until electrostatic equilibrium is achieved.
Properties of Conductors in Electrostatic Equilibrium:
Rapid Redistribution: The time for charges to reach equilibrium is negligible, so conductors quickly stabilize.
Charge Location:
- All excess charge resides on the outer surface of the conductor.
- For a negative net charge, excess electrons accumulate on the surface.
- For a positive net charge, the surface is deficient in electrons, modeled as positive charges residing on the surface.
(a) A charge inside a cavity induces equal and opposite charge on the cavity surface and an equal net charge on the outer surface, independent of its distribution |
(b) a charge outside induces only surface polarization, leaving the cavity charge-free. |
Electric Field Inside: The electric field inside the conductor is zero:
\( \mathrm{E_{inside} = 0} \)
Electric Potential: The conductor is an equipotential object; all points inside and on its surface are at the same potential:
\( \mathrm{V = constant} \)
Surface Electric Field: Just outside the surface, the field is perpendicular and related to surface charge density \(\sigma\):
\( \mathrm{E = \dfrac{\sigma}{\varepsilon_0}} \)
Charge Density Variation: Surface charge density is greater at sharp points or edges than at flat areas. This explains why lightning rods attract lightning discharges.
Polarization in External Fields: In the presence of an external electric field, charges in a conductor redistribute to maintain equilibrium, keeping the surface equipotential.
Hollow Conductors and Electrostatic Shielding:
- Inside a hollow conductor, the electric field is zero if no charges are present inside.
- If a charge is placed in a cavity, an induced charge of equal magnitude and opposite sign appears on the cavity wall, while the remainder resides on the outer surface.
- Electrostatic shielding: A closed conductor blocks external electric fields, creating a field-free region inside (basis of the
Key Principles:
- Excess charges always reside on the surface of conductors in equilibrium.
- The conductor interior has no net charge and no electric field.
- The electric field at the surface is always perpendicular to the surface.
- The conductor is an equipotential surface.
Example :
A spherical conducting shell carries a net charge of \(+8.0 \, \mu C\). Describe the charge distribution and the field inside and outside.
▶️ Answer/Explanation
Step 1: Charges reside only on the outer surface of the sphere.
Step 2: Inside the shell (\(r < R\)), \( \mathrm{E = 0} \).
Step 3: Outside the shell (\(r > R\)), field is as if all charge were concentrated at the center: \( \mathrm{E = \dfrac{1}{4 \pi \varepsilon_0} \dfrac{Q}{r^2}} \).
Final Answer: All charge is on the surface; inside field is zero, outside field is radial outward.
Example :
A conducting sphere has a hollow cavity inside it. A point charge of \( -3.0 \, \mu C\) is placed at the center of the cavity. The conductor itself has a net charge of \(+5.0 \, \mu C\). Find the charge on the inner and outer surfaces.
▶️ Answer/Explanation
Step 1: The charge inside induces \(+3.0 \, \mu C\) on the inner surface of the cavity (to cancel the field in the conductor’s bulk).
Step 2: The remaining charge on the conductor is: \( \mathrm{Q_{outer} = Q_{net} – Q_{inner} = 5.0 – 3.0 = +2.0 \, \mu C} \).
Final Answer: Inner surface = \(+3.0 \, \mu C\); outer surface = \(+2.0 \, \mu C\).