Electric charges are the foundation of electromagnetism. Positive and negative charges interact, with like charges repelling and opposites attracting. This fundamental property shapes the behavior of matter at the atomic level and beyond.

Conservation of charge is a key principle in electrostatics. The total charge in an isolated system remains constant, only transferring between objects. This concept is crucial for understanding electrical interactions and charge distribution in various materials.

Electrical Charges and Conservation of Charge

Properties of electric charges

• Electric charge fundamental property of matter consists of positive and negative charges
• Like charges repel each other while unlike charges attract (protons and electrons)
• Electrons have negative charge $-e$ while protons have positive charge $+e$
  • Neutrons electrically neutral
• Electric charge quantized measured in integer multiples of elementary charge $e = 1.602 \times 10^{-19}$ C
• Net charge of an object sum of its positive and negative charges
  • Objects with equal numbers of protons and electrons electrically neutral (atoms, molecules)

Conservation of charge calculations

• Law of conservation of charge states net charge in isolated system remains constant
  • Charge cannot be created or destroyed only transferred between objects
• When objects brought into contact charge transferred through conduction
  • Electrons mobile charge carriers move from one object to another (metal spheres)
• Amount of charge transferred depends on electrical properties of objects
  • Charge transferred equal in magnitude and opposite in sign for both objects (positive to negative, negative to positive)
• To calculate charge transfer use equation $Q_1 + Q_2 = Q_1' + Q_2'$
  • $Q_1$ and $Q_2$ initial charges, $Q_1'$ and $Q_2'$ final charges after transfer (before and after contact)

Conductors vs insulators

• Conductors materials that allow electric charges to flow easily
  • Metals like copper, silver, and aluminum have loosely bound valence electrons that can move freely
• Insulators materials that do not allow electric charges to flow easily
  • Glass, rubber, and plastic have tightly bound valence electrons that cannot move freely
• Semiconductors have electrical properties between those of conductors and insulators
  • Conductivity can be modified by doping with impurities or applying electric fields (silicon, germanium)
• Dielectrics are insulators that can be polarized by an applied electric field

Polarization and induction charging

• Electric polarization occurs when electric field causes redistribution of charges within an object
  • In conductors free electrons move to one side creating net positive charge on opposite side (electroscope)
  • In insulators electrons shift slightly within atoms creating induced dipoles (water molecules)
• Charging by induction process of charging an object without direct contact
  1. Charged object brought near neutral conductor causing electric polarization
  2. Induced charge distribution remains even after charged object removed
  3. Grounding the conductor allows electrons to flow leaving conductor with net charge opposite to inducing object
• Electrostatic shielding occurs when conductor placed around an object
  • Conductor redistributes charges to cancel external electric field inside shielded region (Faraday cage)
  • Principle used to protect sensitive electronic equipment from external electric fields (circuit boards, cables)

Electric Fields and Electrostatics

• Electric field is a region of space around a charged object where electric forces are exerted on other charges
• Electromagnetic force is one of the fundamental forces of nature, responsible for electric and magnetic interactions
• Electrostatics is the study of stationary electric charges and their interactions
• Triboelectric effect is the transfer of charge between two materials when they are brought into contact and then separated