All equations related to motor

Lenz’s law of motor-

Principle theory of motor 
A current carrying conductor will experience a force when placed in a magnetic field. The conductor can be any metal—iron, copper, aluminum, and so on.

F = IBL sin θ

where
F = force on the conductor (in Newtons)
I = current through the conductor (in amperes)
B = magnetic flux density (in gauss)
L = length of the wire (in meters)
θ = angle between the magnetic field and current

The direction of the force is perpendicular to both the magnetic field and the current.

Picture: Action of force on a wire in a magnetic field.

Electric motor torque is directly proportional to the force on the armature wires.

T = Kt Ia φ

where
T = motor torque
Kt = a constant based on the motor construction
Ia = armature current
φ = magnetic flux

As the armature of motor is rotating in the magnetic field of field winding, according Faraday’s laws of electromagnetic induction a certain voltage also induced in the armature winding.
EMF = KeφS

where
EMF = voltage generated by the turning motor
Ke = a constant based on motor construction
φ = magnetic flux
S = speed of motor (rpm)

This induced voltage will try to cancel out the line voltage, that is it will be of opposite polarity.
The actual voltage available to the armature is the line voltage
minus the CEMF:

VA = Vln – CEMF
where
Va = actual voltage available to the armature
Vln = line voltage supplied to the motor
CEMF = voltage generated within the motor

We can not directly measure Va with a voltmeter because it is an effective voltage inside the armature. However, there is physical evidence that the CEMF exists because the armature current is also reduced

Ia = ( Vln – CEMF)/Ra
where
Ia = armature current
Vln = line voltage to the motor
Ra = armature resistance
CEMF = voltage generated within the motor

The actual relationship between motor speed and CEMF follows
S = CEMF/(Kφ)
where
S = speed of the motor (rpm)
CEMF = voltage generated within the motor
KE = a motor constant
φ = magnetic flux

P = TS
where
P = power
T = torque
S = motor speed

1 hp = 33,000 (ft.lb/min)

Courtesy: eblogbd.com