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MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Electomagnetic Induction Page 2

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4.

Theoretical Deduction of Faraday's Laws

 

Consider a circuit consisting of two parallel rails at a distance L apart, joined by a wire AB which is free to slide along the rails.

In Magnetic Field

 

In the absence of Magnetic Field

 

  • Magnetic field is acting in a perpendicular direction as shown in the fig.
  • When current I is flowing through the wire AB for time dt
    force F = BIl acts on wire AB towards right. (Fleming's left hand rule)
  • The work done in moving a wire AB is dw = fdx = BIldx, if AB moves a distance dx in time dt.
  • Electrical energy supplied by the cell in time dt is E Idt.
  • Electrical energy is utilised in two ways: (i) for producing heat and (ii) remaining spent in doing work. \ EIdt = VIt + dt
  • EIdt = I2 Rdt + BIldx.
  • Substituting ldx = dA and BdA = df
  • EIdt = I2Rdt + Idf

\ E = IR +

df

dt

  •  

\ I = 

E - 

df

dt

 ...(1)

R

 

 

In the absence of magnetic field I =  

E

 ...(2)

 

(Ohm's Law)

R

 

 

Comparing equation (1) and (2) the induced e.m.f. Hence, e = - 

df

.

dt

 

 

5.

E.m.f. Induced in a Straight Conductor

 

(a) Translational Motion:

 

 

In time dt, distance covered by the conductor is dx = vdt
Area swept out
ldx = lvdt
Number of lines of force cut by the conductor =
df = Blvdt

 

Since e = | 

df

 |

dt

 

 

= | 

Blvdt

 | = | Blv |

dt

 

\ e = | Blv |

A straight conductor
moving at right angles to
the magnetic field.

 

 

 

(b) Rotational Motion:

 

In time T (Time for one revolution), area swept out is
dA =
p r2 (r = l = length of the conductor)
Number of lines of force cut by line in one revolution is

df  

=

B dA

\df  

=

B. p r2

 

 

 

e.m.f. induced = e

= | 

df

|

dt

 

 

 

=

Bp r2

T

 

 

 

\ e 

=

Bp r2f

 


Where
f is the frequency of revolution

 

 

6.

Fleming's Right Hand Rule

 

If the thumb, forefinger and middle finger of the right hand are held at right angles to each other so that the forefinger points in the direction of the field, the thumb in the direction of motion of the conductor, then the middle finger gives the direction of the induced e.m.f..

 

7.

Eddy Current

 

Eddy currents are circulating currents induced in a metal block when it is made to moved in and out of a uniform magnetic field or placed in a changing magnetic field.

Disadvantage: Eddy currents produce excessive heating of core in transformers, motors, dynamos, induction coils, etc. This heating effect and energy loss can be minimised if the core is laminated.

Applications: (1) Dead beat galvanometer, (2) Induction furnace, (3) Electric brakes, (4) Induction motor.




 

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