Electrical Engineering ⇒ Topic : Dynamically Induced E.M.F.

Dynamically Induced emf or Motional emf

When a single conductor of length 1 meters moves with a velocity of v m/sec at right angles to uniform magnetic field of flux density B tesla between N and S poles, the emf induced in the conductor is given by e = Blν volts.

If the conductor moves at an angle q to the direction of the magnetic field, the emf induced in the conductor is given by e = Blν sin θ.If the conductor moves parallel to the flux lines, the emf induced in the conductor = O.

Motional emf is associated with energy conversion from electrical to mechanical or mechanical to electrical.

Dynamically Induced E.M.F.

In Figure 1 (a), the conductor A is shown by the cross-section within the uniform magnetic field. It moves at right angle to the magnetic field of flux density B Wb/m². If the conductor moves a length dx in time dt, the area swept by it is equal to I dx where I is the length of the conductor lying within the magnetic field. Here change in flux is equal to BI dx in time dt.

According to Faraday's law, the induced e.m.f. (this e.m.f. is also known as dynamically induced e.m.f.) is given below

                                                                              figure (1)

If the conductor moves at an angle Φ with the magnetic field as shown in Figure 1 (b), the

component of its velocity in the direction perpendicular to the field is given by u sin Φ. Hence,

the induced e.m.f. in this case can be expressed as:

                                       e = Blu sin Φ volts                                                      ............... (1)

If the conductor moves parallel to the field, the value of 0 will be 00 The induced e.m.f. can be written as e = O.

The direction of induced e.m.f. can be found out by Fleming's right hand rule which states that spread the thumb, first finger, and second finger of the right hand at directions mutually perpendicular to each other such that the thumb indicates the direction of rotation of the conductor in the magnetic field, the first finger gives the direction of the magnetic field. The second finger will indicate the direction of the flow of the induced current in the conductor.

                                                                 figure (2)

The DC generators work on the principle of production of dynamically induced e.m.f. in the conductors which are housed in a revolving armature lying within the magnetic field.

  Consider a single conductor of length 1 metres moving at *right angles to a uniform magnetic field of B Wb/m² with a velocity of v m/s [See Figure (a)]. Suppose the conductor moves through a small distance dx in dt seconds. Then area swept by the conductor is = 1 x dx.

      FIGURE (A)                                                         FIGURE (B)

      Flux cut, dΦ = Flux density x Area swept = Bl  dx Wb

According to Faraday's laws of electromagnetic induction, the magnitude of e.m.f. e induced in the conductor is given by ;

Special case: If the conductor moves at angle ∅ to the magnetic field [See Figure (b)], then the velocity at which the conductor moves across the field is *v sin ∅.

The direction of the induced e.m.f. can be determined by Fleming's right-hand rule.

  Consider a single conductor of length 1 metres moving at *right angles to a uniform magnetic field of B Wb/m² with a velocity of v m/s [See Figure (a)]. Suppose the conductor moves through a small distance dx in dt seconds. Then area swept by the conductor is = 1 x dx.

      FIGURE (A)                                                         FIGURE (B)

      Flux cut, dΦ = Flux density x Area swept = Bl  dx Wb

According to Faraday's laws of electromagnetic induction, the magnitude of e.m.f. e induced in the conductor is given by ;

Special case: If the conductor moves at angle ∅ to the magnetic field [See Figure (b)], then the velocity at which the conductor moves across the field is *v sin ∅.

The direction of the induced e.m.f. can be determined by Fleming's right-hand rule.

  Consider a single conductor of length 1 metres moving at *right angles to a uniform magnetic field of B Wb/m² with a velocity of v m/s [See Figure (a)]. Suppose the conductor moves through a small distance dx in dt seconds. Then area swept by the conductor is = 1 x dx.

      FIGURE (A)                                                         FIGURE (B)

      Flux cut, dΦ = Flux density x Area swept = Bl  dx Wb

According to Faraday's laws of electromagnetic induction, the magnitude of e.m.f. e induced in the conductor is given by ;

Special case: If the conductor moves at angle ∅ to the magnetic field [See Figure (b)], then the velocity at which the conductor moves across the field is *v sin ∅.

The direction of the induced e.m.f. can be determined by Fleming's right-hand rule.

  Consider a single conductor of length 1 metres moving at *right angles to a uniform magnetic field of B Wb/m² with a velocity of v m/s [See Figure (a)]. Suppose the conductor moves through a small distance dx in dt seconds. Then area swept by the conductor is = 1 x dx.

      FIGURE (A)                                                         FIGURE (B)

      Flux cut, dΦ = Flux density x Area swept = Bl  dx Wb

According to Faraday's laws of electromagnetic induction, the magnitude of e.m.f. e induced in the conductor is given by ;

Special case: If the conductor moves at angle ∅ to the magnetic field [See Figure (b)], then the velocity at which the conductor moves across the field is *v sin ∅.

The direction of the induced e.m.f. can be determined by Fleming's right-hand rule.

  Consider a single conductor of length 1 metres moving at *right angles to a uniform magnetic field of B Wb/m² with a velocity of v m/s [See Figure (a)]. Suppose the conductor moves through a small distance dx in dt seconds. Then area swept by the conductor is = 1 x dx.

      FIGURE (A)                                                         FIGURE (B)

      Flux cut, dΦ = Flux density x Area swept = Bl  dx Wb

According to Faraday's laws of electromagnetic induction, the magnitude of e.m.f. e induced in the conductor is given by ;

Special case: If the conductor moves at angle ∅ to the magnetic field [See Figure (b)], then the velocity at which the conductor moves across the field is *v sin ∅.

The direction of the induced e.m.f. can be determined by Fleming's right-hand rule.