Electric Charges and FieldsMind Map

Electric charge is a fundamental property of matter responsible for electrostatic force. Charges are of two types: positive and negative. Like charges repel and unlike charges attract. Charge is quantized, meaning any observable charge is an integral multiple of elementary charge e. Charge is also conserved, so total charge of an isolated system remains constant. Conductors allow charges to move freely, while insulators do not. Coulomb’s law gives the force between two stationary point charges: F = kq1q2/r². The force acts along the line joining the charges. For multiple charges, the net force is found by the superposition principle, adding individual forces vectorially.

Electric field describes the influence of a charge in the space around it. It is defined as force per unit positive test charge, E = F/q0. The electric field due to a positive point charge is radially outward, while that due to a negative charge is radially inward. Field is a vector, so for multiple charges the net field is found by vector superposition. Electric field lines are visual tools: their tangent gives field direction and their density indicates field strength. Lines never intersect and begin on positive charges and end on negative charges. Continuous charge distributions such as line, surface and volume charges require integration or Gauss’s law, depending on symmetry.

Electric flux measures the amount of electric field passing through a surface. For a uniform electric field through a plane surface, flux is Φ = EA cosθ, where θ is the angle between the electric field and the area vector. The area vector is always normal to the surface. Flux is maximum when the surface is perpendicular to the field and zero when the surface is parallel to the field. For curved or non-uniform situations, flux is calculated using integration: Φ = ∫E·dA. Through a closed surface, outward flux is taken positive and inward flux negative. Electric flux is central to Gauss’s law, where total closed-surface flux depends only on enclosed charge.

An electric dipole consists of two equal and opposite charges separated by a small distance. Its dipole moment is p = q × 2a, directed from negative charge to positive charge. Dipoles are important because many molecules behave as electric dipoles. The electric field of a dipole is different on its axial and equatorial lines. For a short dipole, axial field is twice the equatorial field in magnitude at the same large distance. In a uniform electric field, a dipole experiences no net force but experiences torque τ = pE sinθ, which tends to align it with the field. Its potential energy is U = -pE cosθ, minimum when aligned with the field.

Gauss’s law states that the total electric flux through any closed surface equals the net charge enclosed divided by permittivity of free space: ∮E·dA = q_enclosed/ε0. The closed surface chosen for applying the law is called a Gaussian surface. Gauss’s law is true for any closed surface, regular or irregular, but it becomes useful for calculating electric field only when symmetry allows E to be constant over parts of the surface. Common useful symmetries are spherical, cylindrical and planar. Charges outside the Gaussian surface may affect electric field at individual points, but their net contribution to total flux through the closed surface is zero.

Applications of Gauss’s law use symmetry to calculate electric fields quickly. For an infinite line charge, cylindrical symmetry gives E = λ/(2πε0r), directed radially outward for positive charge. For an infinite plane sheet, planar symmetry gives E = σ/(2ε0), independent of distance. For a charged spherical shell, field outside behaves as if all charge were concentrated at the centre, while field inside the shell is zero. For conductors in electrostatic equilibrium, electric field inside the conducting material is zero, excess charge lies on the outer surface and field just outside is σ/ε0. Electrostatic shielding works because the field inside a closed conductor is zero.