Flashcards · 9630 · A Level Topic 8

Electric fields and capacitance (A Level) flashcards

21 cards on A Level Topic 8, subtopics 3.8.1 to 3.8.4. Pick a subtopic or study them all.

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Coulomb's law: The force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation: F = Q₁Q₂/(4πε₀r²). Like charges repel; unlike attract.
Value of ε₀ and of 1/(4πε₀): ε₀ = 8.85 × 10⁻¹² F m⁻¹, so 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻². Air can be treated as a vacuum.
Where is the charge on a charged sphere taken to act?: At its centre, so r is measured from the centre of the sphere.
Electrostatic vs gravitational force between a proton and an electron: The electrostatic force is about 2.3 × 10³⁹ times larger. Both are inverse-square, so the ratio does not depend on r; gravity is negligible between subatomic particles.
Charges +1.5 μC and +2.5 μC are 0.20 m apart in air. Force?: F = (1.5 × 10⁻⁶ × 2.5 × 10⁻⁶) ÷ (4π × 8.85 × 10⁻¹² × 0.20²) = 0.84 N, repulsive.

Electric field strength E: The force per unit positive charge at a point: E = F/Q. A vector, in N C⁻¹ (equivalent to V m⁻¹).
Field strength in a uniform field and in a radial field: Uniform (parallel plates): E = V/d. Radial (point charge Q): E = Q/(4πε₀r²).
Derive E = V/d for parallel plates: Work done moving charge Q across the gap: W = Fd = QEd. Also W = QV. So QEd = QV and E = V/d.
Path of a charged particle entering a uniform field at right angles: Constant velocity along the plates (no force that way) and constant acceleration a = QE/m across them, so the path is a parabola.
Field lines between charged parallel plates: Parallel, equally spaced straight lines at right angles to the plates, from positive to negative, bending slightly outwards only at the edges.

Absolute electric potential at a point: The energy transferred per coulomb of positive test charge when a small test charge is moved from infinity to that point. Zero at infinity. Unit V (J C⁻¹).
Potential in a radial field, and work done moving a charge: V = Q/(4πε₀r), keeping the sign of Q. ΔW = QΔV.
Equipotential surface (electric): A surface on which every point has the same potential. No work is done moving a charge along it.
How are E and V related on graphs against r?: E = −ΔV/Δr: E is the gradient of the V–r graph. The area under the E–r graph between two radii gives the potential difference.
Potential vs field strength: Potential is a scalar varying as 1/r; field strength is a vector varying as 1/r². A point of zero potential need not have zero field.

Capacitance: The charge stored per unit potential difference: C = Q/V. Unit farad, F (C V⁻¹).
Capacitance of a parallel-plate capacitor: C = Aε₀ε_r/d, where A is the overlap area, d the plate separation and ε_r the relative permittivity of the dielectric.
Energy stored by a capacitor: E = ½QV = ½CV² = Q²/(2C): the area under a graph of Q against V.
How does a dielectric of polar molecules increase capacitance?: In the field each molecule feels a couple and rotates to align. The aligned molecules produce a field opposing the applied field, so the net field falls. For the same Q the p.d. falls, so C = Q/V rises.
A dielectric is inserted into a capacitor. Isolated vs still connected to the battery: Isolated: Q stays fixed and V falls. Connected: V stays fixed and Q rises.
Energy stored by 100 μF charged to 10 V: ½CV² = ½ × 100 × 10⁻⁶ × 10² = 5.0 × 10⁻³ J.