E.M.F. Is induced in a circuit whenever the amount of magnetic flux linked 3with the circuit is changed as ∅ = BA cos θ the magnetic flux ∅ can be changed by changing B A orθ. Hence there are three methods of producing induced
By changing the magnitude of magnetic field B,
By changing the area A by shrinking or stretching or changing the shape of the coil.
By changing angle θ between the direction of B and normal to the surface area A changing the relative orientation of the surface area and the magnetic field.
The three methods are discussed here briefly.
Induced by changing the magnetic field.
In faraday's experiment motion of the magnet towards the coil increases the magnetic fields B at any point on the wire loop and vice versa. In either case galvanometer shows deflection. Thus induced by changing B.
In faraday's experiment changing current in coil C (on pressing or relapsing key K) changes the magnetic field at any point on coil C. this results in the production of induced in coil C.
Induced by changing the area A motional electromotive force
The conductor loop PQ is free to move without any loss of energy due to friction etc. the crosses represent a uniform magnetic field B which is perpendicular to the plane of the paper and directed inwards.
Let the conductor PQ be moved towards the left with a constant velocity. The area enclosed by the loop PQRS decreases. Therefore amount of magnetic flux linked with the loop decrease. An deflection in the galvanometer G connected in the loop.
If the length RQ = x and
PQ = RS = l, then
Magnetic flux linked with the loop PQRS
∅ = B/x
As x is changing with time the amount of magnetic flux linked with the loop changes. Therefore an is induced It the loop given by
E = - d∅ / dt = - d/dt (B/x)
E = B I (-dx / dt) = B/v
Where - dx / dt = v is the speed of the conductor PQ.
E is called motional electromotive force.
According to Lenz's law the direction of e is along QRSP
The expression for motional can also be obtained using Lorentz force equation.
Consider any arbitrary change q in the conductor PQ. As the conductor moves change q also moves with speed u in the magnetic field B. Lorentz force on this charge = q u B. according to Fleming's left hand rule the direction of this force is towards Q.
Work done in moving the charge from P to Q is W = Qv B x 1
As is work done per unit charge.
Therefore e = W / q = q u B x I / q
E = B l v
If R is resistance of the loop the induced current l would be given by
I = e / R = B l u / R
The direction of induc3d current is given by Fleming's right hand rule or Lenz's law.
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