Govt. Exams
Entrance Exams
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
Using Gauss's law with cylindrical surface: E × 2πr = λL/ε₀, hence E = λ/(2πε₀r)
After contact: charge on each = (Q - 3Q)/2 = -Q. Force F = k(-Q)(-Q)/r² = kQ²/r², attractive (opposite signs).
By symmetry, radial components cancel. Axial component: E = kQx/(a² + x²)^(3/2)
Connected spheres have same potential. V = kQ/r, so Q ∝ r. Both statements are equivalent and correct.
