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Electric Field
A region where charged particles experience force due to other charges.
Coulomb's Law
Describes the electric field (E) generated by a point charge (Q) as E = k |Q| / r².
Superposition Principle
The total electric field is the vector sum of fields from all individual charges.
Continuous Charge Distribution
Electric field from a continuous charge is found by integrating contributions from infinitesimal charge elements.
Electric Field of an Infinite Line of Charge
The electric field due to an infinite line of charge is given by E = 2k |λ| / r.
Electric Field of an Infinite Plane of Charge
An infinite plane generates a constant electric field, E = σ / (2ε₀).
Electric Field Inside a Uniformly Charged Sphere
Inside a uniformly charged sphere, the electric field is zero (E = 0).
Electric Field Outside a Uniformly Charged Sphere
Outside the sphere, it behaves as if all charge were concentrated at the center: E = kQ / r².
Dipole Moment
A dipole has a dipole moment defined as p = qd, where q is charge and d is the separation distance.
Electric Field Along a Dipole Axis
The field along the dipole axis is E = (1/4πε₀) (2p / r³).
Electric Field Perpendicular to Dipole Axis
The field perpendicular to the dipole axis is E = (1/4πε₀) (p / r³).
Gauss's Law
Relates electric flux through a surface to the enclosed charge: Φₑ = Qₑₙc / ε₀.
Electric Field in Conductors
Inside a conductor in electrostatic equilibrium, the electric field is zero (E = 0).
Electric Field Just Outside a Conductor
Just outside a conductor's surface the field is E = σ / ε₀, directed perpendicular to the surface.
Capacitor Electric Field
The electric field between capacitor plates is uniform and given by E = V / d.
Capacitance Energy Storage
Energy stored in a capacitor’s electric field is U = (1/2) C V².
Magnitude and Direction of Electric Fields
Electric fields are vector quantities with both magnitude and direction.
Radial Direction of Electric Fields
Electric fields point radially outward from positive charges and inward toward negative charges.
Field Strength Independence in Infinite Plane
The field strength generated by an infinite plane is independent of the distance from the plane.
Field Strength Dependence in Infinite Line of Charge
The field strength from an infinite line of charge depends only on the perpendicular distance from the line.
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