Unit 8: Electric Charge, Fields, and Gauss’s Law

Unit 8 - Electric Charges Fields and Gauss's Law.pdf 

Electric Charge

Electric force is a fundamental force—like gravity—but it can attract or repel.

Charge is symbolized by q, measured in Coulombs (C).

Elementary charge (e) = 1.602 × 10⁻¹⁹ C

• Proton: +e

• Electron: –e

Coulomb's Law

• Describes the force between two point charges:

• Similar to Newton's law of gravity (inverse square law)

Charging by Induction

• A charged object near a neutral conductor causes electrons to rearrange.

• This creates an attractive force, even without contact.

• If you separate the conductor during induction, each piece can retain a net charge.

Electric Field (E)

• An electric field is the effect a charge has on the space around it.

• Direction is defined by the force on a positive test charge.

• Field strength is shown by line density in field diagrams.

• Electric field from a point charge:

Electric Field from Continuous Distributions

• Use calculus to sum contributions from all small charges

• Charge densities:

  • Linear (λ): q per length (C/m)

  • Surface (σ): q per area (C/m²)

  • Volume (ρ): q per volume (C/m³)

Electric Flux (Φₑ)

• Measures how much electric field passes through a surface: Φₑ= EAcosθ

• Net flux through a closed surface:

Gauss’s Law

• Great shortcut for calculating electric fields with symmetry!

• Total flux through a closed surface equals the enclosed charge

Examples with Gauss's Law