Govt. Exams
Conductivity σ = 1/ρ where ρ is resistivity. Since resistivity is in Ω·m, conductivity is in (Ω·m)⁻¹ = S/m or mho/meter.
For uniform field between parallel plates: V = Ed = 100 × 0.02 = 2 V.
Potential energy of two point charges is U = kq₁q₂/r. This is positive for like charges (repulsive) and negative for unlike charges (attractive).
By Gauss's law, for r > R, the electric field depends only on the enclosed charge Q and is E = kQ/r², independent of the outer shell.
The torque on a dipole in a uniform field is τ = p × E = pE sin θ, which tends to align the dipole with the field.
Electric potential due to a point charge is V = kq/r, where k is Coulomb's constant. This is a fundamental relationship in electrostatics.
With dielectric, C = κε₀A/d where κ is relative permittivity of dielectric
Surface area = 4πR². Surface charge density σ = Q/(4πR²)
By Gauss's law, Φ = Q_enclosed/ε₀ = (2q - q + 3q)/ε₀ = 4q/ε₀
Electric field is negative gradient of potential: E = -∇V or E = -dV/dr in one dimension
