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Flashcards · AP® Physics 2: Algebra-Based · Unit 10

Unit 10: Electric Force, Field, and Potential flashcards

47 cards on topics 10.1 to 10.7. Pick a topic or study the whole unit.

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10.1 Electric Charge and Electric Force

What is the elementary charge and why is charge quantized?
e = 1.60 × 10⁻¹⁹ C is the smallest charge that exists on its own. Proton +e, electron −e, neutron 0. Any charge is q = Ne with N a whole number, so 1.5e is impossible.
What is Coulomb's law?
F = k|q₁q₂|/r², with k = 9.0 × 10⁹ N·m²/C² = 1/(4πε₀). The force acts along the line joining the charges; like charges repel, unlike attract.
The distance between two point charges is halved. How does the force change?
It becomes 4 times larger, since F ∝ 1/r². Tripling one charge and tripling the distance gives 3/9 = 1/3 of the force.
A large charge and a small charge interact. Which feels the bigger force?
Neither. The two forces are a third-law pair: equal in size and opposite in direction.
How do you find the net electric force from several charges?
Find each pair force with Coulomb's law using |q₁q₂|, get its direction from a diagram, then add as vectors using components.
Why does gravity, not the electric force, govern the Moon's orbit?
The electric force is far stronger between particles, but Earth and the Moon are almost exactly neutral, so their electric force is nearly zero. Gravity only attracts and never cancels.
What does it mean for an object to be neutral?
It has equal amounts of positive and negative charge, not zero charges.

10.2 Conservation of Electric Charge and the Process of Charging

What is conservation of charge?
A system's net charge is constant unless charge moves in or out; any change is matched by an opposite change in the surroundings. In solids, charging means moving electrons, not protons.
Identical metal spheres with +6 nC and −2 nC touch and separate. What is the charge on each?
Add with signs, then share equally: (+6 − 2)/2 = +2 nC each. Equal sharing applies only to identical conductors.
How do you charge a sphere by induction?
Bring the rod near, ground the sphere, break the ground connection, then remove the rod. The sphere ends with the opposite sign to the rod. Removing the rod first leaves it neutral.
Does attraction prove that an object is charged?
No. A charged object attracts a neutral one by inducing charge separation or polarization (the opposite charge is nearer). Only repulsion proves like charges.
What happens when two materials are rubbed together?
Electrons move from one material to the other, so they end with equal and opposite charges. Negative means electrons gained; positive means electrons lost.
What is grounding?
Connecting an object to Earth, a huge, nearly neutral system that can give or take electrons without its own charge changing noticeably.
An object gains 1.0 × 10¹⁰ electrons. What is its charge?
q = −Ne = −1.0 × 10¹⁰ × 1.60 × 10⁻¹⁹ = −1.6 × 10⁻⁹ C.

10.3 Electric Fields

What is the electric field?
The force per unit charge on a small test charge: E = F_E/q, in N/C. It is a vector, pointing outward from a lone positive charge and inward towards a lone negative one.
What is the field of a point charge?
E = k|q|/r², where q is the source charge (not the test charge) and r is from the charge, or from the centre of a charged sphere for points outside it.
Which way is the force on an electron in an electric field?
Opposite to E. F_E = qE, so a negative charge is pushed against the field direction.
How do you read field lines?
The tangent gives the field direction, closer lines mean a stronger field, and lines never cross. They show the force direction, not the path of a charge.
What is the electric field inside a conductor in equilibrium?
Zero. Any excess charge sits on the surface, and the field just outside is perpendicular to the surface.
The field 0.10 m from a point charge is 1200 N/C. What is it 0.20 m away?
E ∝ 1/r², so doubling r gives a quarter: 300 N/C.
How do you find the net field from several charges?
Add the individual fields as vectors, using x- and y-components. Do not add magnitudes of fields that point in different directions.

10.4 Electric Potential Energy

What is the electric potential energy of two point charges?
U_E = kq₁q₂/r, with signs, zero at infinite separation. It belongs to the system, not one charge, and equals the external work to bring the charges slowly from infinity.
What is the sign of U_E for like and unlike charges?
Like charges: positive (you must push them together). Unlike charges: negative (you must add energy to separate them). Negative means less energy than at infinite separation.
How do you find the potential energy of three or four charges?
Add U_E for every pair: 3 charges make 3 pairs and 4 charges make 6 pairs, including diagonals. Do not count a pair twice.
How does U_E depend on separation compared with the force?
Energy goes as 1/r; force goes as 1/r². Tripling r makes U_E one third: +0.50 J becomes about +0.167 J.
What is U_E for +2.0 nC and −3.0 nC that are 0.020 m apart?
U_E = 9.0 × 10⁹ × (2.0 × 10⁻⁹)(−3.0 × 10⁻⁹) / 0.020 = −2.7 × 10⁻⁶ J.
When does external work equal the change in electric potential energy?
When the charges start and end at rest, so no kinetic energy is gained: W_ext = ΔU_E.

10.5 Electric Potential

What is electric potential?
V = U_E/q, the potential energy per unit charge at a point, in volts (1 V = 1 J/C). It belongs to the point, not the test charge, and is zero infinitely far away.
How do you find the potential from several point charges?
V = Σkqᵢ/rᵢ, keeping each sign. V is a scalar: no components or angles, and use r, not r².
How are field and potential related?
|E| = |ΔV/Δr| along the field, in V/m (= N/C). E points towards decreasing V. Two equipotentials 12 V apart and 4.0 mm apart give 3.0 × 10³ V/m.
What are equipotential lines?
Lines of equal potential, always perpendicular to the field. Closely spaced lines mean a strong field. The field does no work on a charge moved along one.
Does V = 0 at a point mean E = 0 there?
No. Midway between +q and −q, V = 0 but E is not zero.
Two conductors are joined by a wire. What becomes equal?
Their potential, not their charge. Electrons move until the surfaces are at the same potential; a conductor in equilibrium is at one potential throughout.
Which way does a charge released at rest move in terms of potential?
Positive: towards lower V (along E). Negative: towards higher V (against E). Both lose potential energy.

10.6 Capacitors

What is capacitance?
C = Q/ΔV, the charge stored per volt, in farads (1 F = 1 C/V). Q is the charge on one plate. C depends only on geometry and the material between the plates, not on Q or ΔV.
What is the capacitance of a parallel-plate capacitor?
C = κε₀A/d, with ε₀ = 8.85 × 10⁻¹² C²/(N·m²), A the area of one plate and d the gap in metres. Plates 0.025 m² and 1.0 mm apart in air give about 221 pF.
How much energy does a capacitor store?
U_C = ½QΔV = ½C(ΔV)² = Q²/(2C), the area under the Q–ΔV graph. A 10 µF capacitor at 20 V stores ½ × 10 × 10⁻⁶ × 400 = 2.0 × 10⁻³ J.
What is the field between the plates of a parallel-plate capacitor?
Uniform, from + to −, with E = ΔV/d (edge effects ignored). A charged particle there has constant acceleration qE/m and follows a parabola like a projectile.
A dielectric is inserted into an isolated charged capacitor. What changes?
Q is fixed. C rises by κ, so ΔV, E and stored energy all fall by κ.
A dielectric is inserted into a capacitor connected to a battery. What changes?
ΔV is fixed. C rises by κ, so Q and stored energy rise by κ; the field between the plates is the same.
How does a dielectric increase capacitance?
It polarizes, setting up an induced field opposite to the plates' field. The net field drops, so more charge is stored per volt: C rises by κ.

10.7 Conservation of Electric Energy

How much does a charge's potential energy change when it moves through a potential difference?
ΔU_E = qΔV, with the sign of q and ΔV = V_f − V_i. Only the end points matter, not the path.
How fast is a particle after accelerating from rest through a potential difference?
If only electric forces act, ΔK = −ΔU_E, so ½mv² = |q||ΔV| and v = √(2|q||ΔV|/m).
A proton starts from rest and crosses 100 V. What are its kinetic energy and speed?
K = eΔV = 1.6 × 10⁻¹⁹ × 100 = 1.6 × 10⁻¹⁷ J. v = √(2K/m) ≈ 1.38 × 10⁵ m/s.
An electron and a proton cross the same potential difference from rest. Which gains more kinetic energy?
Neither: ΔK depends on |q|, which is the same, not on mass. The lighter electron ends up much faster.
A −5.0 nC charge moves from −20 V to +30 V. What is ΔU_E?
ΔU_E = qΔV = (−5.0 × 10⁻⁹)(+50) = −2.5 × 10⁻⁷ J. A negative charge has lower potential energy at higher potential.
How do you include an outside force in electric energy conservation?
ΔK + ΔU_E = W_ext. Use either W_field = −qΔV or ΔU_E for the field's effect, never both.

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