Understanding Electromagnetism

• Electromagnetism is the science of electric charge, forces, and fields associated with electric charge.

Aspects of Electromagnetism:

• Electricity involves electric forces produced by electric charges, whether at rest or in motion.
• Magnetism deals with magnetic forces produced only by moving charges, acting solely on other moving charges.
• Electrostatics are interactions between electric charges at rest or nearly so.
• Static electricity effects are explained by a physical quantity called electric charge.
• There are two types of charge: positive and negative.
• Like charges repel, unlike charges attract.
• The force between charges decreases with distance.

Structure of Matter

• Atoms consist of negatively charged electrons, positively charged protons, and uncharged neutrons.
• Protons and neutrons form a small, dense core called the nucleus, surrounded by electrons.
• The atomic number is the number of protons or electrons in a neutral atom of an element.
• Ionization is the gain or loss of electrons.
• A positive ion forms when one or more electrons are removed.
• A negative ion forms when an atom gains one or more electrons.

Electric Charge

• When the number of protons in a macroscopic body equals the number of electrons, the total charge is zero, and the body is electrically neutral.
• Excess negative charge is created by adding negative charges or removing positive charges from a neutral body.
• Excess positive charge is created by adding positive charge or removing negative charge.
• The algebraic sum of all electric charges in a closed system is constant.
  • This is the principle of conservation of charge.
  • The total electric charge on two bodies together does not change. - Charge is not created or destroyed in any charging process, it is merely transferred.
• The magnitude of charge of the electron or proton is a natural unit of charge.
• Conductors permit electric charge to move easily, while others do not.
• Conductors have free electrons, allowing charge to move freely.
• Superconductors allow charge movement without energy loss.
• Insulators do not allow charges to move through them.
  • Insulators have no, or very few, free electrons.
• Semiconductors have properties between conductors and insulators.

Induced Charges

• Induction is a technique where a body gives another a charge of opposite sign without losing its own charge.
• An uncharged metal ball on an insulating stand has free electrons that repel from a nearby negatively charged rod and shift away from the rod.
• Electrons cannot escape due to the insulating stand and surrounding air. Excess negative charge accumulates on the ball's right surface, with a deficiency of negative charge (net positive charge) on the left surface.
• These excess charges are called induced charges.

Coulomb's Law

• The electric force magnitude between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
• Magnitude F of the force that each of two point charges q1 and q2 a distance r apart exerts on the other: F = k |q1q2| / r^2.
• k is a proportionality constant.
• The SI unit of electric charge is the coulomb (C).
• Magnitude of the charge of an electron or a proton e = 1.602176565(35) × 10-19 C.

Electric Field

• This is the electric force exerted by the electric field created by other charged bodies on a charged body.

Electric field lines

• Electric field is electric force per unit charge.
• Test charge, q0, measures the electric field strength.
• The unit of electric-field magnitude is 1 newton per coulomb (1 N/C).
• The electric field of a point charge points away from a positive charge and toward a negative charge.
• The electric field is described by electric field lines.
• Electric field lines show direction of electric field at each point.
• Spacing shows general electric field magnitude. - Strong = lines close together - Weaker = lines far apart
• At any particular point, the electric field has a unique direction.
  • This means so only one field line can pass through each point, they never intersect.
• Description of electric interactions include:
  • A given charge distribution acts as a source of electric field.
  • the electric field exerts a force on any charge.

Electric Dipoles

• Electric dipole is a pair of point charges with equal magnitude and opposite sign separated by a distance d.
• The net force on an electric dipole in a uniform external electric field is zero.
• The two forces F+ and F- on the dipole have magnitude qE but opposite directions and add to zero.
  • But cannot be the same line so torques don't all add to 0.
• Torque: T = pEsin ф where ф is the is angle between p and E and Magnitude of electric dipole moment p- *the product of the charge q and the separation d is the magnitude of a quantity called the electric dipole moment
• Units of are charge times distrance C-m

Electric Flux

• Electric flux is a measure of the “flow” of electric field through a surface.
• It equals the product of an area element and the perpendicular component of E, integrated over a surface.
• F = E • A electric flux for uniform E.
• The SI unit for electric flux is 1 N • m²/C.

Gauss's Law

• The total electric flux through a closed surface (surface integral of the component of E normal to the surface), equals a constant times the total charge Qencl enclosed by the surface.
• Gauss's Law is logically equivalent to Coulomb's Law.
  • The use Gauss's law greatly simplifies problems with symmetry.

Electric field of various symmetric charge distributions

• Electric fields caused by several symmetric charge distributions

Gauss's Law - Charges on Conductors

• When excess charge is placed on a solid conductor and it is at rest, charge resides entirely on its surface, with E = 0 everywhere.
• In any conductor, flux can be positive or negative
  • Choosing the positive electric field is radially outward and the electric field is radially inward is negative.
• The field just outside a charged conductor is perpendicular to the surface, and its perpendicular component E₁ is equal to σ/εο.