Govt. Exams
By Gauss's law, electric field inside a uniformly charged spherical shell is zero everywhere
When identical conducting spheres touch, charge distributes equally. Final charge on each = (Q₁ + Q₂)/2 by charge conservation
Torque on dipole in uniform field: τ = p × E = pE sinθ, where θ is angle between dipole moment and field
By Gauss's law: Φ = Q/ε₀ = 10 × 10⁻⁶ / (8.85 × 10⁻¹²) = 1.13 × 10⁶ N·m²/C
Capacitance with dielectric: C = Kε₀A/d, where K is the dielectric constant. The dielectric increases capacitance by a factor of K
Inside a conductor in electrostatic equilibrium, the electric field is always zero regardless of position or charge distribution
V' = k(2q)/(r/2) = 4kq/r = 4V. Doubling charge increases V by 2×, halving distance increases V by 2×, total effect is 4×
For a dipole configuration, the electric field at the midpoint is E = 2kq/r² directed from negative to positive charge. E = 2 × 9 × 10⁹ × 2 × 10⁻⁶ / (0.05)² = 7.2 × 10⁶ N/C
For isothermal process: W = nRT ln(V_f/V_i) = P₁V₁ ln(3V₁/V₁) = P₁V₁ ln(3)
For constant pressure: Q = n·Cp·ΔT. For diatomic gas, Cp = (7/2)R. Q = 3 × (7/2) × 8.314 × (600-300) = 3 × 3.5 × 8.314 × 300 = 26,194 × 2.85 ≈ 74,826 J
