A circular coil of radius 4m with the speed 35m/s is moving in a magnetic field perpendicular to it. If induced emf is of 60 V, then the value of magnetic field applied is 

CONCEPT:

• Motional emf: The emf induced due to motion relative to a magnetic field is called the motional emf. 

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• 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   is the speed of the conductor PQ​

CALCULATION:

Given, length of the wire (l) = 2πr = 2π × 4 = 8π, magnetic field (B) = 4.5 Wb/m2, Induced emf (ε) = 60 V and velocity (v) =35 m/s

• The emf induced in the coil can be calculated as

⇒ ε = Blv

The above equation can be written for magnetic field (B) as

1. Hence option 2) is correct.