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Flashcards · AP® Physics C: Electricity and Magnetism · Unit 10

Unit 10: Conductors and Capacitors flashcards

30 cards on topics 10.1 to 10.4. Pick a topic or study the whole unit.

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10.1 Electrostatics with Conductors

Why is the field zero inside a conductor in electrostatic equilibrium?
Free charges inside move whenever there is a field, and they keep moving until their own field cancels the applied field inside; this happens effectively at once. By Gauss's law there is then no net charge inside, so all excess charge is on the surface.
Why is a conductor in equilibrium an equipotential?
E = 0 inside, so ΔV = −∫E·dl = 0 between any two points. The whole conductor, surface included, is at one potential, which need not be zero.
What is the field just outside a conducting surface?
E = σ/ε₀, perpendicular to the surface. Compare an isolated thin sheet, which gives σ/(2ε₀).
Where is the charge density greatest on a conductor?
At points and edges, so the field is strongest there. Only an isolated sphere has uniform surface charge density.
Where does charge go when a charge q is placed in a cavity inside a conductor of net charge Q?
The cavity wall carries −q and the outer surface carries Q + q. An empty cavity has no charge on its wall and E = 0 inside it.
How does a closed conducting shell shield its interior?
Charges induced on its outer surface cancel any outside field everywhere within it, so an empty cavity is field-free. A charge inside still produces a field outside unless the shell is grounded.
What happens to a conductor placed in an external field?
It polarizes: induced negative and positive charges appear on opposite sides, the net charge is unchanged, and the field inside the metal stays zero.
A metal sphere is at 500 V. What is the potential at its center?
500 V. The whole conductor is an equipotential, so V is constant, not zero, inside.

10.2 Redistribution of Charge Between Conductors

What happens when two conductors are connected?
They become one conductor and reach a single potential, effectively instantly. Total charge is conserved. Positive charge flows from high V to low V; electrons move the other way.
How do two distant spheres joined by a thin wire share charge?
Equal potential gives q₁/R₁ = q₂/R₂, so q₁ = QR₁/(R₁ + R₂). Spheres of radii 1.0 cm and 4.0 cm sharing 10 nC hold 2.0 nC and 8.0 nC.
Which of two connected spheres has the stronger surface field?
The smaller one. σ₁/σ₂ = E₁/E₂ = R₂/R₁, since E = V/R at each surface.
What is ground in circuit and electrostatics problems?
An ideal reference at V = 0 that can absorb or supply any amount of charge without changing its potential.
Does grounding always leave a conductor with zero charge?
Only if it is isolated. A grounded conductor near a charge keeps an induced charge of opposite sign; for a grounded sphere of radius R with charge q at distance d, Q′ = −qR/d.
What happens when a charged conductor touches the inside of a hollow conductor surrounding it?
It loses all its charge to the outer surface of the hollow conductor.
How do you keep an induced charge on a grounded conductor?
Break the ground connection first, then remove the nearby charge. The wrong order lets the charge flow back.

10.3 Capacitors

What is capacitance?
C = Q/ΔV, the charge on each conductor per unit potential difference, in farads (1 F = 1 C/V). It depends only on shape, size and the gap material, not on Q or ΔV.
What is the capacitance of a parallel-plate capacitor?
C = ε₀A/d, from E = σ/ε₀ = Q/(ε₀A) between the plates and ΔV = Ed. With a dielectric filling the gap, C = κε₀A/d.
Why is the field between parallel plates σ/ε₀?
Each plate's sheet field is σ/(2ε₀). Between the plates the two fields add to σ/ε₀; outside they cancel. Edge fringing is ignored.
What is the general method for finding capacitance of any shape?
Assume charges ±Q, use Gauss's law to find E, integrate E to find ΔV, then C = Q/ΔV.
What are the capacitances of spherical and cylindrical capacitors?
Concentric spheres (a inner, b outer): C = 4πε₀ab/(b − a), giving 4πε₀a as b → ∞. Coaxial cylinders of length L: C = 2πε₀L/ln(b/a).
How much energy does a capacitor store?
U = ∫(q/C)dq = Q²/(2C) = ½QΔV = ½C(ΔV)². Not QΔV: charging stores only half of that.
What should you ask first when a capacitor is changed?
What is fixed. Isolated: Q is fixed. Connected to a battery: ΔV is fixed. Doubling the gap of an isolated capacitor leaves E unchanged and doubles U.
How does a charged particle move between parallel plates?
It has constant acceleration a = qE/m across the gap, so it follows projectile-style parabolic motion. Gravity is negligible for electrons, protons and ions.

10.4 Dielectrics

What is a dielectric?
An insulator whose bound charges shift slightly in a field, so it polarizes. Non-polar molecules gain induced dipoles; polar molecules partly line up.
Why does a dielectric reduce the field between capacitor plates?
Bound charge appears on its faces (negative next to the positive plate), and its field opposes the applied field. The net field is smaller but not zero: E = E₀/κ for an isolated capacitor.
What is the dielectric constant?
κ = ε/ε₀, with no unit. κ = 1 for a vacuum, about 1.0006 for air, larger for other insulators.
How does a dielectric change capacitance?
Filling the gap multiplies C by κ for any capacitor shape. Parallel plates: C = κε₀A/d = εA/d.
What happens when a dielectric is inserted in an isolated capacitor?
Q is fixed, so ΔV, E and U = Q²/(2C) are all divided by κ. An isolated capacitor at 30 V filled with κ = 3.0 drops to 10 V.
What happens when a dielectric is inserted with the battery connected?
ΔV is fixed, so Q and U are multiplied by κ, while E = ΔV/d is unchanged.
What is the induced surface charge density on a dielectric?
σᵢ = σ(1 − 1/κ), where σ is the free charge density on the plates. The bound charge stays in the dielectric and is not free charge.

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