E) at the axis of the infinitely long solenoid

,

where N – the number of wire coils in the solenoid; L – the length of the solenoid; n ₀ – the quantity of coils on the unit of solenoid length.

The superposition principle: the magnetic field created with one current is independent from positions of other currents. Then the resultant vector of magnetic intensity is a vector sum of magnetic intensity vectors of individual currents:

,

therefore: 1) the direction of the resultant vector is defined by parallelogram rule of the vectors’ additions; 2) the magnitude of the resultant vector is defined with cosine theorem:

,

where a – angle between the vectors.

The relation between magnetic induction and magnetic intensity :

,

where m₀=4p× 10^–7 H/m – permeability of vacuum; m – magnetic permeability (for air m=1).