Class 12 Physics Electromagnetic Induction Varying Area in a moving loop

Methods of producing Induced Emf in a circuit: Varying Area(A)in a moving loop

If the area within the magnetic field changes, then emf will be induced.

• The rectangular loop enters the magnetic field and goes out of the field.
• Initially there is no magnetic field from where the loop is starting, the moment the loop enters the magnetic field it experiences the change in the magnetic field at the boundary.
• When the loop was inside the magnetic field there was no change in the magnetic flux.
• But when the loop leaves the region of magnetic field there was decrease in the magnetic flux.
• Because when it leaves the magnetic field area keeps on decreasing.
• As area decreases therefore flux also decreases.
• At both the boundaries there is change in the area,as a result there is change in the flux.

Therefore there will be induced current at the boundary.   Mathematically:-

• The emf which is induced is known as Motional emf because this emf is induced due to the motion of the conductors.
• Consider a conductor is moving out of the magnetic field with some velocity ‘v’.
• The part which is inside the field =’X’ and length of the conductor=’length
• In time Δt, loop covers small distance Δx.
• Decrease in the area =-(length Δx),
• Where (-) ive sign shows decrease in area.
• Decrease in flux = dΦ =B.ΔA =-BlengthΔx where ΔA=change in area
• Therefore from Faraday’s Lenz’s law, Induced emf e= -(dΦ/dt)
• =d/dt(BlengthΔx)
• => Blength (Δx/Δt)
• Therefore Motional Emfe= Blengthv
• where (velocity) v= Δx/Δt
• Induced current =I=(e/R) =(Blengthv/R)
• where R=resistance of the loop
• Motional Emf comes into play when the area of the loop within the magnetic field changes. Brakes of the fast moving trains

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