Electric Charge and Charging Methods

• Electric charge is a material's property that causes it to exert electrostatic force on other materials, either repelling or attracting them.

Types of Charge

• Negative charge occurs when a body has extra electrons.
• Positive charge occurs when a body has fewer electrons compared to protons.
• A positively charged body loses electrons.
• A negatively charged body gains electrons.
• A negatively charged body's mass increases slightly.
• A positively charged body's mass decreases slightly.

Charge on Particles:

• Electron: -1.6 x 10^-19 Coulombs
• Proton: +1.6 x 10^-19 Coulombs

Mass of Particles

• Neutron > Proton > Electron.
• Neutron has no charge (neutral).
• Three methods to charge a body: friction, conduction, and induction.
• bodies are rubbed together, electrons transfer from one to the other, charging the bodies.
• Conduction: Charging through contact.
• Induction: Charging without contact.
• A metal sphere can be charged by bringing a charged rod nearby, inducing charge separation, and then grounding the sphere to leave it with the opposite charge

Basic Properties of Charge

Additivity:

• Total charge in a system is the algebraic sum of individual charges, without considering direction.

Conservation:

• Charge can neither be created nor destroyed, only transferred.

Quantization:

• Charge is transferred in fixed quantities, as integer multiples of the charge on an electron; charge (q) = n * e (where n is an integer).

Coulomb's Law:

• Describes the force between two charges: F = k * q1 * q2 / r^2.
• Where: k = 1 / (4 * pi * epsilon_0) = 9 x 10^9 Nm^2/C^2.
• R is the distance between the charges.
• Epsilon_0 is the permittivity of free space (8.854 x 10^-12 C^2/Nm^2)
• Coolomb's Law unit relationship:
  • N⋅m^2/C^2=1/(4⋅π⋅ε0)

Coulomb's Law in Vector Form:

• Force is a vector quantity, requiring direction.
• f12 (vector) implies the force on charge 1 by charge 2
• Unit vector r21(vector) indicates direction from r2 to r1
• r21 = r1(vector) - r2(vector)

Dielectric Constant K:

• Ratio of electric force in vacuum to that in a medium: K = F_vacuum / F_medium
• It is also the ratio of permittivity of a medium to permittivity of vacuum: K = epsilon / epsilon_0; this is known as relative permittivity.
• Medium: F = 1 / (4 * pi * K * epsilon_0) * q1 * q2 / r^2
• A medium with a K value of 2 reduces the force between charges to half of what it is in a vacuum

Electric Field Lines:

• Imaginary lines representing the electric field in a medium where the Tangent at any point gives the direction of force on a positive charge placed at that point
  • Lines point outward from isolated positive charges.
  • Lines point inward to isolated negative charges.
  • Lines go from positive to negative in a dipole.

Properties of Electric Field Lines:

• Start from positive charges and end at negative charges. the Lines are continuous curves
• Electric field lines are perpendicular to metal surfaces.
• No two electric field lines intersect each other.

Force on a Charge in an Electric Field:

• F = q * E, where: E = F / q (test charge).

Dipole:

• Combination of equal and opposite chances
• Usually at the distance of 2a or 2l

Dipole Moment:

• p = q * 2a (or 2l). it indicates the strength
• Direction: from negative to positive charge,
• It is a vector quantity.

Electric Field

Due to a Point Charge:

• E = k * q / r^2

Due to a Dipole

• on the axial point
• E = k * 2p / r^3

For Equidorial Point

• E_equidorial = okp/r^3
• Electric field is a factor of two greater than at the equatorial point: EXIAL = 2(E equitorial)

Electric Field Calculations

• When calculating the electric field between two charges, assess the direction; fields in the same direction add, opposite directions subtract.
• Distance measurements will usually be from the individual charges

Electric Flux:

• Number of electric field lines passing perpendicularly through a surface.
• Indicates the electric field strength and its spread through an area.

Electric Flux Formula:

• Φ = E * A * cos(θ), where: θ is the angle between the electric field and the area vector.
• Can also be written as:
  • Φ = ∮ E⋅dS for an area, using surface normal vector

Gauss's Law:

Gauss's Law Key Facts:

• The electric flux through any closed surface is proportional to the enclosed electric charge.
• Applies only to closed surfaces.
• Not applicable when not closed
• If not closed consider a Gaussian surface which is symmetrical around the charge and hence one can apply the Gauss law.
• Φ = Q_enclosed / epsilon_0
• For a large integration: phi = INTe⋅dsvector = q and close/Epsilon naught
• Flux can be positive/negative/0
• If lines coming outside then positive
• Coming insight then negative
• Coming insight through outside then 0

Applications of Gauss's Law

Electric Field Due to an Infinitely Long Charged Wire:

• Enclose the wire in a cylindrical Gaussian surface
• (E) exists on the curved surface making an angle of 0 degree, E=0 and the other surfaces which makes an angle of 90 degree
• Relationship: E = λ / (2 * pi * epsilon_0 * r)
• Where λ is the linear charge density.

Electric Field Due to a Charged Sheet:

• Model: E= sigma/ 2 Epsilon not Here, use Cylindrical Gaussian surface and the electric field will be calculated from the 2 surfaces.
• The Electric field in charge sheet sigma by total epsilon not and this implies distance independent.
• If you have similar sheet so, consider 3 areas around and 1 area between the 2 sheets, Electric fields will be calculated.

Electric Field on a Conducting Sphere:

• All charge given to conducting sphere behaves as if it is at sphere

Three Important Conditions:

• Outside E = KQ / r^2
• On surface E= sigma /Epsilon Not
• Inside sphere E = zero (charge insdie=0)

Electric Field on a Ring Due to its Axis:

• Formula: E = kq X / (I^2 + x^2) raised to 3/2

Torque on a Dipole in an Electric Field:

• τ = p * E * sin(θ)
• Stable equilibrium: dipole aligns with field (0 degrees)
• Unstable equilibrium: dipole opposes field (180 degrees)
• Torque and Stable and unstable portions are explained.

Understand electric charge as a material property causing electrostatic forces. Explore the types of charge: negative (excess electrons) and positive (fewer electrons). Learn about charging methods including friction, conduction, and induction.