Govt. Exams
Using Gauss's law for an infinite plane: E = σ/(2ε₀). The field is independent of distance and perpendicular to the plane.
By Gauss's law, for a uniformly charged spherical shell, the electric field inside (r < R) is zero because the enclosed charge is zero.
When identical conducting spheres touch, charge distributes equally. Total charge = +Q + (-Q) = 0, so each gets 0. They remain neutral after separation.
Work done by electric field = Change in kinetic energy. W = qEd = eEd, which equals kinetic energy since initial KE = 0.
For a conducting sphere, V₀ = kQ/a = kσ(4πa²)/a, which gives σ = V₀/(ka).
In series, 1/C_eq = 1/2 + 1/3 + 1/6 = 1. C_eq = 1 μF. Q = C_eq × V = 1 × 12 = 12 μC. Same charge on all capacitors.
Perpendicular to field: uniform motion. Parallel to field: constant acceleration. Combined motion is parabolic (similar to projectile motion).
U = kq₁q₂/r. When distance doubles, U becomes kq₁q₂/2r = U/2
Field due to each plate is σ/2ε₀. Between opposite plates, fields add: σ/2ε₀ + σ/2ε₀ = σ/ε₀
E = -dV/dr = -d(kr²)/dr = -2kr. Field is negative indicating direction opposite to increasing r.
