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 µr. When the solenoid carries a current of I amperes, a magnetic field of flux µi/l/ µo µra 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/ µo µra di/dt = - µ2 µr µoa.di/dt