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A wire of length 3m is moving with a speed of 50m/s in a direction perpendicular to a magnetic field of 4.5 Wb/m2. The  induced emf in the wire is
  • a)
    675 × 10V
  • b)
    675 V
  • c)
    675 mV
  • d)
    675 × 105V
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A wire of length 3m is moving with a speed of 50m/s in a direction per...
Motional emf: The emf induced due to motion relative to a magnetic field is called the motional emf. 
  • Consider a straight conductor PQ moving perpendicular to a uniform magnetic field B.
    • Assume the motion of the rod to be uniform with a constant velocity of (v m/s).
    • The rectangle PQRS forms a closed circuit enclosing a changing area due to the motion of the rod PQ.
  • The magnetic flux ϕ enclosed by the loop PQRS can be given as:
⇒ ϕ = B × area = B × (l.x)
  • Since the conductor is moving, there is a change in the rate of area moving. This causes a rate of change of flux which induces an emf.
  • This induced emf is given by:

Where - dx/dt = v is the speed of the conductor PQ​
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A wire of length 3m is moving with a speed of 50m/s in a direction perpendicular to a magnetic field of 4.5 Wb/m2. The induced emf in the wire isa)675 × 102Vb)675 Vc)675 mVd)675 × 105VCorrect answer is option 'B'. Can you explain this answer?
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