The back EMF in a DC motor opposes the supply voltage. This is explained by _______.

The back EMF in a DC motor opposes the supply voltage. This is explained by Lenz's law.

1.) Lenz's law

The negative sign in Lenz’s law indicates that the induced emf in the coil is in the opposite direction of the magnetic flux, which is linked with the coil.

\(E=-N{d\phi\over dt}\)

2.) Fleming's Left-Hand Rule

Fleming’s Left-hand rule states that if the thumb, forefinger, and middle finger of the left hand are stretched into mutually perpendicular directions such that the index finger and middle finger of a stretched left hand direct the magnetic field and electric current respectively then the thumb shows the direction of motion or force acting on the conductor. The directions of electric current, magnetic field, and force are similar to three mutually perpendicular axes, i.e. x, y, and z-axes.

3.) Fleming's Right Hand Rule

Fleming’s Right Hand Rule states that if we arrange our thumb, forefinger, and middle finger of the right hand perpendicular to each other, then the thumb points toward the direction of the motion of the conductor relative to the magnetic field, the forefinger points toward the direction of the magnetic field and the middle finger points towards the direction of the induced current.

4.) Faraday’s law

 Faraday's Law states that the magnitude of the induced EMF in a conductor is directly proportional to the rate of change of magnetic flux linkage. 

\(E=N{d\phi\over dt}\)