Q. What is meant by dynamically induced emf and statically induced emf? On what factors do these depend? Derive eq. for these two emfs.

Sol. Dynamically induced emf:

Consider a conductor of length l m placed in a uniform magnetic field of density B wb/m².

Let this conductor be moved with velocity Vm/sec in the direction of field. In this case no flux is cut by conductor, therefore. No emf is induced.

Now if this conductor is moved with the velocity v m/s in a direction perpendicular to its own length and perpendicular to the direction of the magnetic field. Flux is cut by conductor therefore, an emf is induced in the conductor.

Area swept per sec. by the conductor = l × v m²/sec

Flux cut per sec. = flux density × area swept per sec. = Blv

Rate of change of flux, d φ/dt

Flux cut per sec. = Blv wb/sec

Induced emf, e = d φ/dt = Blv volts

The magnitude of emf induced is proportional to the components of the velocity in a direction perpendicular  to the direction of the magnetic field and induced emf is given by

        E = Blv sinθ volts

 Statically induced emf

 Self induced emf :

 Consider a solenoid of N turns, length l m, area of x- section a square meters and of relatively permeability µ_r. When the solenoid carries a current of I amperes, a magnetic field of flux µ_i/l/ µ_o µ_ra weber is set up around the solenoid and links with it.

If the current flowing through the solenoid is changed., the flux produced by it will change and therefore, an emf will be induced.

               Self induced emf e = -µ dΦ/dt

                           = - µ d/dt [µ/l/ µ_o µ_ra di/dt = - µ² µ_r µ_oa.di/dt