It is based on the principle that when a current-carrying conductor is placed in a magnetic field, it experiences a mechanical force whose direction is given by Fleming's Left-hand rule and whose magnitude is given by
Force, F = B I l Newton
Where, B is the magnetic field in weber/m2.
I is the current in amperes and
l is the length of the coil in meter.
Turning or twisting force about an axis is called torque.
Consider a wheel of radius R meters acted upon by a circumferential force F Newton’s as shown in above figure. The wheel is rotating at a speed of N rpm.
The angular speed of the wheel ω = 2πN/60 rad/sec
Work done in one revolution W= Force x distanced travelled in one revolution
W = FX2πR joules
Power developed, P = Work done/time = W/Time for 1 rev.
P = FX2πR/(60/N) = (FXR)(2πN/60)
P = T x ω watts
Power in armature = armature torque x ω
EbIa = Ta x (2ΠN/60)
Where, Ta = Armature torque.
Eb = PΦZN/60A
Substituting Eb values, we get,
Ta = 0.159ΦIa (PZ/A) N-m