Engineering Physics

Electrostatics: Electric Field and Charge Interaction

• Coulomb's Law gives force between two point charges.F = (1/(4πε0)) * q1*q2 / r^2 * r̂.
• Principle of Superposition states that the net electric field is the vector sum of fields produced by all charges.
• Electric Field at a point is the force per unit positive test charge:E = F/q.

Diagram to paste: electric-field.png

Electrostatic Potential and Potential Energy

• Electrostatic Potential V is the work done per unit charge in bringing a test charge from infinity to a point in the field.
• Relation between potential and field:E = -∇V.
• Potential Energy of a charge system equals the work needed to assemble charges from infinity.
• Potential Gradient gives the spatial rate of change of potential and points in the direction of maximum decrease of potential.

Diagram to paste: potential-surface.png

Electric Flux, Displacement Vector and Gauss' Law

• Electric Flux:Φ = ∬ E·dS. Represents the number of field lines passing through a surface.
• Electric Displacement Vector D relates to free charge in materials and helps simplify field calculations in dielectrics.
• Gauss' Law in integral form:∮ E·dS = Q_enclosed / ε0.
• Gauss' Law in differential form:∇·E = ρ / ε0.
• Derivation of Coulomb's Law from Gauss' Law uses spherical symmetry around a point charge to obtain the inverse square relationship.

Diagrams to paste: gauss-law.png, flux-surface.png

Magnetostatics: Magnetic Field and Force

• Magnetic Field B describes the magnetic influence at a point in space.
• Magnetic Flux:Φ_B = ∬ B·dS.
• Magnetic Flux Density is another name for B, measured in Tesla.
• Lorentz Force on a moving charge:F = q(E + v × B).

Diagram to paste: lorentz-force.png

Biot Savart Law

• Gives magnetic field produced by a steady current element. Common applications include long straight conductors and circular current loops.
• Basis for deriving magnetic fields in symmetric current distributions.

Diagram to paste: biot-savart.png

Ampere's Circuital Law

• Integral form:∮ B·dl = μ0 I_enclosed.
• Used for finding B in systems with high symmetry such as solenoids, toroids and long straight conductors.
• Complements Biot Savart Law in steady current situations.

Diagram to paste: ampere-law.png

Gauss' Law for Magnetism

• States that the net magnetic flux through any closed surface is zero:∮ B·dS = 0.
• Differential form: ∇·B = 0.
• Implies that magnetic monopoles do not exist.

Equation of Continuity

• Expresses conservation of charge:∂ρ/∂t + ∇·J = 0.
• Links time variation of charge density with divergence of current density.

Diagram to paste: continuity-equation.png