Govt. Exams
Potential energy of dipole in electric field: U = -p·E = -pE cos θ. Minimum at θ = 0 (aligned).
Using Coulomb's law and symmetry, the radial components cancel. The axial component gives E = kQx/(x² + R²)^(3/2).
Electric force is conservative; work depends only on initial and final positions (potentials), not on the path taken. W = q(V_initial - V_final).
Two capacitors C in parallel: C_parallel = 2C. This in series with C: C_eq = (2C × C)/(2C + C) = 2C/3.
If there were a tangential component of electric field at the surface, charges would move tangentially, violating electrostatic equilibrium. Thus, only the normal component exists.
By Gauss's law, the field outside depends on the total enclosed charge Q + q. The field is E = k(Q + q)/r² for r > R.
Dielectrics in series combine like capacitors in series. Total capacitance = (ε₀A × 2K₁K₂)/(d(K₁ + K₂)) = C₀ × 2K₁K₂/(K₁ + K₂).
For an electric dipole, the field along the perpendicular bisector is maximum at distance d = a/√2, where 2a is the separation between charges. Here, a = 1 m, so maximum field is at 1/√2 m.
The electric field just outside a conductor in a dielectric medium is E = σ/(Kε₀), so it decreases by the factor of dielectric constant K compared to vacuum.
U = ½C'V'² where C' = KC and V' = 2V. So U = ½(KC)(2V)² = 4CKV²
