Coulomb's Law and Electric Force

• Electric charge is the property that enables a body or particle to produce and experience electric effects.

Coulomb's Law and Force due to Multiple Charges

• F = (1 / 4πε₀εᵣ) * (q₁q₂ / d²), where:
  • ε₀ represents the permittivity of free space, vacuum, or air
  • εᵣ is the relative permittivity or dielectric constant of the medium
  • εᵣ = ε / ε₀
  • ε₀ = 8.857 x 10⁻¹² C² / Nm² or farad / metre
  • 1 / 4πε₀ = 9 x 10⁹ Nm²/C²
• The electric force on charge q₁ due to q₂ is F₁ = (1 / 4πε₀εᵣ) * (q₁q₂ / |r₁ - r₂|³) * (r₁ - r₂) where r₁ and r₂ are the position vectors
• Similarly, the electric force on charge q₂ due to charge q₁ is F₂ = (1 / 4πε₀εᵣ) * (q₁q₂ / |r₂ - r₁|³) * (r₂ - r₁)
• Substitute q₁ and q₂ with their signs.

Identical Charges Suspended from a Common Point

• Two small bodies with equal charge and mass suspended by strings from a common point
• Coulomb's law: Fₑ = k(qq / r²), where k = 9 x 10⁹ Nm²/C²
• k(qq / r²) = mg tan θ
• To determine the charge on the bodies, equate horizontal and vertical components of the forces: k(qq / r²) = mg tan θ
• q = r * √(mg tan θ / k)

Electric Field

• Electric field refers to the space around an electric charge where electric influence is felt.
• It is a conservative field

Motion of a Charged Particle in a Uniform Electric Field

• A charged body with mass 'm' and charge 'q', initially at rest, in a uniform electric field of intensity E experiences a force F = Fq
• The direction of F aligns with E if 'q' is positive, and it is opposite to E if 'q' is negative.
• The body moves in a straight line with uniform acceleration a = Eq/m and initial velocity u = 0
• At time t, its final velocity v = u + at = (Eq/m)t
• Displacement s = ut + (1/2)at² = (1/2)(Eq/m)t²
• Momentum p = mv = (Eq/m)t
• Kinetic energy K.E = (1/2)mv² = (1/2) (L²q² / m) t²

Electric Field due to a Uniformly Charged Non-Conducting Sphere

• At any point inside the sphere: E = (1 / 4πε₀) * (Qr / R³) for r < R
• On the surface of the sphere: E = (1 / 4πε₀) * (q / R²)
• At any point outside the sphere: E = (1 / 4πε₀) * (q / r²)

Electric Field at the Axis of a Circular Uniformly Charged Ring

• Intensity of electric field at a point P on the axis of the ring, at distance x from its center: E= (1 / 4πε₀) * (qx / (a² + x²)^(3/2)

Electric Dipole

• An electric dipole consists of a pair of equal and opposite point charges q and -q, separated by a distance 2a

Electric Dipole Moment (p)

• Electric dipole moment is the product of the magnitude of either charge and the distance between the two charges: p = q(2a)