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Electric Field Concepts

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Electric Field Strength

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The electric field strength at a point is the force experienced per unit positive charge placed at that point. Formula: E=FqE = \frac{F}{q}, where EE is the electric field strength, FF is the force, and qq is the charge.

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Dielectric Constant

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The dielectric constant is the ratio of the absolute permittivity of a material to the vacuum permittivity. Formula: k=εε0k = \frac{\varepsilon}{\varepsilon_0}, where kk is the dielectric constant, ε\varepsilon is the absolute permittivity, and ε0\varepsilon_0 is the vacuum permittivity.

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Coulomb's Law

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Coulomb's Law describes the electrostatic force between two charged particles. Formula: F=keq1q2r2F = k_e \frac{|q_1q_2|}{r^2} where FF is the force, kek_e is Coulomb's constant, q1q_1 and q2q_2 are the charges, and rr is the distance between the charges.

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Electric Potential Energy

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Electric potential energy is the work done to bring a charge from infinity to a point in space in an electric field. Formula: U=keqQrU = k_e \frac{qQ}{r}, where UU is the potential energy, qq is the test charge, QQ is the source charge, and rr is the separation.

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Permittivity

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Permittivity is a measure of how much electric field is 'allowed' to permeate a medium. Formula (for vacuum): ε0=8.854×1012 F/m\varepsilon_0 = 8.854 \times 10^{-12} \text{ F/m}, where ε0\varepsilon_0 is the permittivity of free space, also known as the electric constant.

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Electric Dipole Moment

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The electric dipole moment is a measure of the separation of positive and negative charges in a system. Formula: p=qd\vec{p} = q \vec{d}, where p\vec{p} is the dipole moment, qq is the magnitude of one of the charges, and d\vec{d} is the displacement vector pointing from the negative to the positive charge.

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Faraday's Law of Induction

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Faraday's law of induction states that the induced electromotive force in any closed circuit is equal to the negative of the rate of change of the magnetic flux through the circuit. Formula: E=dΦBdt\mathcal{E} = -\frac{d\Phi_B}{dt}, where E\mathcal{E} is the electromotive force (EMF) and ΦB\Phi_B is the magnetic flux.

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Electric Potential

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Electric potential is the amount of electric potential energy per unit charge at a point in an electric field. Formula: V=Uq=keQrV = \frac{U}{q} = k_e \frac{Q}{r}, where VV is the electric potential, UU is the potential energy, and rr is the distance from the charge.

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Capacitance

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Capacitance is a measure of a component's ability to store charge. Formula: C=QVC = \frac{Q}{V}, where CC is the capacitance, QQ is the charge, and VV is the voltage across the component.

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Gauss's Law

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Gauss's Law relates the electric field flux through a closed surface to the charge enclosed by that surface. Formula:

ΦE=SEdA=Qencε0\Phi_E = \oint_{S} \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\varepsilon_0}
, where ΦE\Phi_E is the electric flux, E\vec{E} is the electric field, dAd\vec{A} is the vector area, QencQ_{\text{enc}} is the enclosed charge, and ε0\varepsilon_0 is the permittivity of free space.

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