Electric charge is a fundamental property of matter. Two types of electric charge:

• Positive charge (protons)

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The total electric charge in an isolated system remains constant. $\sum q_{initial} = \sum q_{final}$ Implications:

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Electric flux through a surface is measure of electric field passing through it. $\Phi_E = \int \vec{E} \cdot d\vec{A} = \int E\,dA\cos\theta$ Where:

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The dot product $\vec{E} \cdot d\vec{A}$ projects E onto surface normal. $\vec{E} \cdot d\vec{A} = |\vec{E}||d\vec{A}|\cos\theta$ Physical meaning:

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Energy of system of charges due to their positions relative to each other. $U = \text{potential energy of charge system}$ For two point charges:

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Electric force is conservative (path-independent work). $W_{A \to B} = -\Delta U = U_A - U_B$ For electric field:

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When conductors reach electrostatic equilibrium: Properties:

• All excess charge resides on surface

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Hollow conductor shields interior from external electric fields. Properties:

• E = 0 inside hollow conductor

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Electric current is rate of charge flow through a cross-section. $I = \frac{dq}{dt}$ Units: Amperes (A) = Coulombs/second (C/s)

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Current density (vector): $\vec{J} = nq\vec{v}_d$ Units: A/m2

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Force on moving charge in electric and magnetic fields: $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$ For magnetic field only:

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Perpendicular to field (v ⊥ B):

• Circular motion (magnetic force provides centripetal)
• Speed constant (force ⟂ velocity -> no work)

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Changing magnetic flux induces electromotive force (emf). Motional emf (conductor moving in static field): $\mathcal{E} = \oint (\vec{v} \times \vec{B}) \cdot d\vec{l}$

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Self-inductance L:

• Changing current in coil induces emf in same coil
• $\mathcal{E} = -L\frac{dI}{dt}$

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