AP Physics C: E&M - Core Concepts & Laws

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Coulomb's Law (Formula & Vector Form)

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Describes the electric force between two point charges. **Formula:** $F_e = k_e \frac{|q_1 q_2|}{r^2}$ **Vector Form:** $\vec{F}_{12} = k_e \frac{q_1 q_2}{r^2} \hat{r}_{21}$ * $k_e$: Coulomb's constant ($\approx 8.99 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2$) * $q$: Charges * $r$: Distance between centers * Like charges repel; opposite charges attract.

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Principle of Charge Conservation

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The net electric charge of an isolated system remains constant during any physical process. Charge can be transferred from one object to another (via conduction or induction), but the total algebraic sum of the charges in the system does not change. For example, in beta decay, a neutron turns into a proton, but a new electron is created simultaneously to balance the charge.

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Quantization of Electric Charge

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Electric charge exists in discrete packets rather than a continuous spectrum. **Formula:** $q = ne$ * $n$: Integer (positive or negative) * $e$: Elementary charge ($\approx 1.602 \times 10^{-19} \, \text{C}$) The charge of a single electron or proton is the smallest indivisible unit of free charge.

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Electric Field ($E$) Definition

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A vector field representing the force per unit charge exerted on a positive test charge placed at a point in space. **Formula:** $\vec{E} = \frac{\vec{F}_e}{q_0}$ **SI Unit:** Newtons per Coulomb (N/C) or Volts per meter (V/m). * **Direction:** Points away from positive source charges and toward negative source charges.

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Electric Field of a Point Charge

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The electric field magnitude produced by a single isolated charge $q$ at a distance $r$. **Formula:** $E = \frac{k_e |q|}{r^2}$ Derived from Coulomb's Law by dividing by the test charge magnitude. This follows an **inverse-square law**, similar to gravity. The field is radial: outward for $+q$, inward for $-q$.