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Flashcards · AP® Physics C: Electricity and Magnetism · Unit 9

Unit 9: Electric Potential flashcards

23 cards on topics 9.1 to 9.3. Pick a topic or study the whole unit.

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9.1 Electric Potential Energy

What is the electric potential energy of two point charges?
U = kq₁q₂/r = q₁q₂/(4πε₀r), with U = 0 at infinite separation. Substitute charges with their signs: like charges give positive U, unlike negative.
How is electric potential energy defined?
The work an external force does to bring the charges slowly from infinitely far apart to their present separation: U(R) = ∫_∞^R (−kq₁q₂/r²) dr. It belongs to the system, not one charge.
How do you find the potential energy of a system of several charges?
Add kqᵢqⱼ/rᵢⱼ once for each pair: N charges make N(N − 1)/2 pairs. Three equal charges +q on a triangle of side a give U = 3kq²/a.
How is force found from potential energy?
F_r = −dU/dr. The force is minus the slope of the U(r) graph, not its height.
How are external work and electric work related to ΔU?
Moving charges between rest states, W_ext = ΔU and W_electric = −ΔU. They have opposite signs.
How do U and F scale with separation for two point charges?
U ∝ 1/r and F ∝ 1/r². Doubling r halves U and reduces F to a quarter.
What happens to U when like charges are released from rest?
They repel and move apart, so U falls toward zero, converted to kinetic energy.

9.2 Electric Potential

What is electric potential?
The potential energy per unit charge a test charge would have at a point: V = U/q, in volts (1 V = 1 J/C). It is a scalar that depends only on the source charges.
What is the potential of a point charge and of several point charges?
V = kq/r for one charge, with V = 0 at infinity. For several, add as scalars with signs: V = Σkqᵢ/rᵢ. No components.
How do you get potential difference from the electric field?
V_B − V_A = −∫_A^B E·dl. In a uniform field, ΔV = −EΔx. Potential falls in the direction of E.
How do you get the electric field from potential?
E_x = −dV/dx: the field is minus the slope of V, pointing from high to low potential. 1 V/m = 1 N/C.
Does V = 0 at a point mean E = 0 there?
No. E depends on the slope of V, not its value. Midway between +q and −q, V = 0 but E is not zero.
What are equipotentials?
Surfaces of equal potential. They are perpendicular to field lines, and no work is done moving a charge along one.
What is the potential of a ring on its axis and of an arc at its center?
Ring: V = kQ/√(R² + x²). Any arc at its center: V = kQ/R, since every piece is at distance R and V is a scalar sum.
Why can't V be set to zero at infinity for an infinite line charge?
Its potential diverges. Use differences only: V(a) − V(b) = (λ/2πε₀) ln(b/a).

9.3 Conservation of Electric Energy

How does a charge's potential energy change when it moves between two potentials?
ΔU = qΔV = q(V_f − V_i). Keep the signs of q and ΔV.
How much kinetic energy does a charge gain if only the electric force acts?
ΔK = −ΔU = −qΔV, since K + U is constant. With other forces, W_ext = ΔK + ΔU.
What is the speed of a charge accelerated from rest through a potential difference?
v = √(2|q||ΔV|/m). K ∝ ΔV but v ∝ √ΔV, so a 9 times larger ΔV gives 3 times the speed.
What is an electronvolt?
1 eV = 1.602 × 10⁻¹⁹ J, the energy one elementary charge gains through 1 V. Convert to joules before using ½mv².
Which way do electrons accelerate in a potential?
Toward higher potential. A charge released from rest moves so its potential energy decreases, and for a negative charge that means moving to higher V.
Does the path matter for the energy change of a charge?
No. The electrostatic force is conservative, so only the end potentials matter, not the path or the plate separation.
What happens at a turning point for a charge moving in a potential?
K = 0 and U equals the total energy, so the charge reverses. A proton with 50 eV facing a rise to +60 V turns back where V = +50 V.
How is energy shared when two free charges fly apart?
Total momentum stays constant and K_total = −ΔU. The lighter object gets more of the kinetic energy.

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