On an equipotential surface, the work involved in transporting a charge from one point to another is zero. If the electric field is not normal, there will be a non-zero component along the surface, requiring work to move a charge on an equipotential surface.
Self Inductance of a long air-cored solenoid: Consider a long air solenoid having `n' number of turns per unit length. If current in solenoid is I , then magnetic field within the solenoid, B =μₒnI...(1) where μₒ= 4π x 10⁻⁷ henry/metre is the permeability of free space. If A is cross-sectional area of solenoid, then effective flux linked with solenoid of length ‘l’ where N = nl is the number of turns in length 'l' of solenoid. <p> <p>
Φ =(nl BA) Substituting the value of B from (1) Φ = nl(μₒnI ) A =μₒn² AlI ...(2) Self inductance of air solenoid L = Φ/I = μₒn² Al ......(3) If N is the total number of turns in length l, then n = N/l Therefore, self inductance L = μₒ(N/l)²Al = μₒ N² A/l ....(4)
