vault backup: 2026-09-06 23:41:08
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[[physics]]
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[[Electric Force, Field, and Potential]]
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# Summary
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* Measured in capacitance ($C=\frac{Q}{\Delta V}$), value fixed by physical build $C=\kappa \epsilon_0\frac{A}{d}$
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* Field between plates is uniform except near edges. $E_C=\frac{Q}{\kappa \epsilon_0 A}$ (equal to $\frac{\Delta V}{d}$)
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* Charged particle between plates feels constant force. Projectile with constant accel.
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* Stored energy written as: $U_C=\frac{1}{2}Q\Delta V=\frac{1}{2}C(\Delta V)^2=\frac{Q^2}{2C}$.
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* Adding dielectric raises capacitance by factor of $\kappa$, sets up induced field inside dielectric that opposes plate field.
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* On AP exam, only parallel plate capacitors required, edge effects ignored unless stated otherwise.
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[[Electric Force, Field, and Potential]]
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# Summary
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* Change in electric potential energy for charge moving between 2 potentials $\Delta U_E=q\Delta V$ (J)
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* q can be positive or negative. $\Delta V=V_{final}-V_{initial}$.
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* Energy is conserved: $\Delta K=-\Delta U_E$
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* Positive charges speed up moving towards lower potential. Negative charges speed up moving towards higher potential.
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* Electric field points towards decreasing potential.
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* For particle starting at rest, kinetic energy gained equals magnitude of $q\Delta V$, lets you solve for final speed.
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[[Electric Force, Field, and Potential]]
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# Summary
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* Charge is quantized, integer multiple of $e=1.6x10^{-19}$.
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* $q=\pm ne$
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* Coulomb's law: $F=k\frac{p_1p_2}{n^2}$; directly proportional to charge, inversely proportional to distance.
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* Same signs repel, opposite signs attract.
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* Electric force is stronger than gravity for tiny particles, gravity controls large scale because big objects are usually neutral.
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* Electric permittivity measures how much a material polarizes in a field. Conductors let charge move freely, insulators don't.
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* Only need to calculate force for 4 or less interacting charges unless situation is highly symmetrical.
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[[Electric Force, Field, and Potential]]
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# Summary
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* Electric field at a point = electric force on a positive test charge divided by charge = $\vec E=\frac{\vec F_E}{q}$ (unit N/C).
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* Test charge's impact on field is negligible.
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* Field lines point towards negative and away from positive. Closer lines = stronger field.
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* Net field from several charges is sum of vectors.
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* Inside a conductor in electrostatic equilibrium field is zero. Charge sits on surface, surface field is perpendicular to surface.
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* Inside a charged insulator inside can be nonzero since charge stays instead of moving to surface.
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[[Electric Force, Field, and Potential]]
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# Summary
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* Electric potential energy is work required from external force to assemble charges from infinity. Infinity set is the zero reference.
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* Elastic potential energy: $U_E=\frac{1}{4\pi \epsilon_0}\frac{q_1q_2}{r}=k\frac{q_1q_2}{r}$
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* Positive $U_E$ means repulsive interaction from like charges.
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* Negative $U_E$ means attractive interaction from unlike charges.
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* For multiple charges, add potential energy of each pair.
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* $U_E$ is a scalar.
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* Energy is conserved, as charges move potential is traded for kinetic.
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[[Electric Force, Field, and Potential]]
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# Summary
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* Electric potential is energy per charge: $V=\Delta U_E/q$ (Volts)
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* Potential comes from multiple point charges added as scalars.
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* Potential can be positive or negative, reference set at infinity.
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* Electric field points towards decreasing potential. $|\vec E|=|\Delta V/\Delta r|$
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* Equipotent lines (isolines) are perpendicular to field vectors. No work is done moving charge along equipotent.
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* Conductors in electrical contact redistribute charge on the surface until it sits at the same potential.
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[[Electric Force, Field, and Potential]]
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# Summary
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* Net charge changes only when charge travels in and out of a system.
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* Charging usually happens through electron transfer.
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* Induced charge separation polarizes an object without contact. Happens in neutral conductors and insulators.
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* In conservation problems, charge of separated objects should sum to charge of system.
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* Grounding occurs when a system connects to a large neutral object.
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* Conductors let electrons move easily, insulators only let bound charges shift slightly.
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* Main 3 ways to charge: friction induction contact.
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[[Thermodynamics]]
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* Energy required to change temperature: $Q=mc\Delta T$
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* Rate of conduction: $\frac{Q}{\Delta t}=\frac{kA\Delta T}{L}$
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* Specific heat ($c$) is intrinsic and determines the amount of energy required to change temperature.
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* Thermal conductivity is also intrinsic, metals conduct well, insulators don't.
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[[Thermodynamics]]
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* Energy required to change temperature: $Q=mc\Delta T$
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* Rate of conduction: $\frac{Q}{\Delta t}=\frac{kA\Delta T}{L}$
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* Specific heat ($c$) is intrinsic and determines the amount of energy required to change temperature.
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* Thermal conductivity is also intrinsic, metals conduct well, insulators don't.
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