Electromagnetic Induction - 3

Fleming’s Right hand rule:

On sleeching yours right hand’s thumb, the index finger and middle finger is such a way that thumb reresents direction of motion of conductor, the index finger ther direction of magnetic field, then the middle finger represents the direction of the induced current.


Time varying magnetic field:

If a conducting loop is placed inside a time varying magnetic field, te changing magnetic field acts as a source of electric field and hence induce an e.m.f., infact the electric field is ever induced when no conductor is present

Can be used to determine that electric field. Where is different from an electrostatic field, as it is non conservative. We cannot define the potential corresponding to this field in the usual sense, that is, dV = .... not hold hex. has ... have a direction shown when is incoming because has to be negative when is positive.


Illustration: Consider a cylindrical magnetic field which increases with time. Find out electric field at a distance r from its centre when
(1) r < R
(2) r > R



Ans: (1) When r < R



Due to symmetry E at every part is same.
Using    
        => E.2r = - r²
             (for cylindrical region only)

(2) For (r > R)



Using
          E.2r = - r²
      


SELF INDUCTANCE:

(1) First definition:

If a coil with N turns and current I be considered.
Totl Flux = N_B is directly proportional to current, that is:
N_B i
The constant of this proportionality is called L (the self inductance).



(2) Second definition:

I changing current in a circuit causes a change in the magnetic flux which induces E.M.F.. This E.M.F. is proprtional to the rate of chage of current. Thus
E -


Dumb Question: How to find potential difference across an inductor ?

Ans: We can find the direction of self induced e.m.f. across an inductor from Lenz's law. The induced e.m.f. is produced whenever there is a change in the current in the inductor. This e.m.f. always acts to oppose this change figure shows these cases. Assume that the inductor is ideal so, V_aL - V_a - V_b is equal to magnitude of self induced e.m.f.




Illustration: Find the self inductance of an ideal solenoid ?
(Assume require quantities)

Ans: For is solunoid of length l and cross sectional area. A having number of turns N, the flux linked I_g is given by N.
Where is flux linked by each turn.
=> N = nlBA       (n = N/l)
The magnetic induction of a solunoid is given by
     B = µ₀nI
=> N = µn²lAI
But, N = LI
this gives LI = µ₀lAI
              L = µ₀n²lA
where n = N/l = Number of turns per unit length.


Mutual Inductance:

A Changing current is one circuit causes a changing magnetic flux and an induced e.m.f. in a neighburing circuit.
This e.m.f. is proportional to the rate of change of current in the first circuit.
The proportionality factor is called mutual inductance.



    E₁
or E₁ = -
Also, M =
The sign is a reflection of Lenz's law.


Dumb Question: What is the series and parallel combination of inductor ?

Ans: (a) In series



l_eff = l₁ + l₂

(b) In parallel



l_eff =